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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 102960.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.ci1 | 102960dj8 | \([0, 0, 0, -150768003, -400611519358]\) | \(126929854754212758768001/50235797102795981820\) | \(150003286376195156978810880\) | \([2]\) | \(31850496\) | \(3.7211\) | |
| 102960.ci2 | 102960dj6 | \([0, 0, 0, -131601603, -580902177598]\) | \(84415028961834287121601/30783551683856400\) | \(91919192791168268697600\) | \([2, 2]\) | \(15925248\) | \(3.3745\) | |
| 102960.ci3 | 102960dj3 | \([0, 0, 0, -131590083, -581008993342]\) | \(84392862605474684114881/11228954880\) | \(33529479608401920\) | \([2]\) | \(7962624\) | \(3.0280\) | |
| 102960.ci4 | 102960dj7 | \([0, 0, 0, -112619523, -754356628222]\) | \(-52902632853833942200321/51713453577420277500\) | \(-154415544966919709890560000\) | \([2]\) | \(31850496\) | \(3.7211\) | |
| 102960.ci5 | 102960dj5 | \([0, 0, 0, -67953603, 215587569602]\) | \(11621808143080380273601/1335706803288000\) | \(3988399143309115392000\) | \([2]\) | \(10616832\) | \(3.1718\) | |
| 102960.ci6 | 102960dj2 | \([0, 0, 0, -4593603, 2786673602]\) | \(3590017885052913601/954068544000000\) | \(2848833407287296000000\) | \([2, 2]\) | \(5308416\) | \(2.8252\) | |
| 102960.ci7 | 102960dj1 | \([0, 0, 0, -1644483, -776453182]\) | \(164711681450297281/8097103872000\) | \(24177822608130048000\) | \([2]\) | \(2654208\) | \(2.4787\) | \(\Gamma_0(N)\)-optimal |
| 102960.ci8 | 102960dj4 | \([0, 0, 0, 11580477, 18025891778]\) | \(57519563401957999679/80296734375000000\) | \(-239764764096000000000000\) | \([2]\) | \(10616832\) | \(3.1718\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.ci do not have complex multiplication.Modular form 102960.2.a.ci
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
