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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 14800.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14800.i1 | 14800q3 | \([0, 1, 0, -2110008, 1179003988]\) | \(16232905099479601/4052240\) | \(259343360000000\) | \([2]\) | \(165888\) | \(2.1414\) | |
| 14800.i2 | 14800q4 | \([0, 1, 0, -2102008, 1188395988]\) | \(-16048965315233521/256572640900\) | \(-16420649017600000000\) | \([2]\) | \(331776\) | \(2.4879\) | |
| 14800.i3 | 14800q1 | \([0, 1, 0, -30008, 1083988]\) | \(46694890801/18944000\) | \(1212416000000000\) | \([2]\) | \(55296\) | \(1.5921\) | \(\Gamma_0(N)\)-optimal |
| 14800.i4 | 14800q2 | \([0, 1, 0, 97992, 7995988]\) | \(1625964918479/1369000000\) | \(-87616000000000000\) | \([2]\) | \(110592\) | \(1.9386\) |
Rank
sage: E.rank()
The elliptic curves in class 14800.i have rank \(0\).
Complex multiplication
The elliptic curves in class 14800.i do not have complex multiplication.Modular form 14800.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
