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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 70560bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.dy3 | 70560bt1 | \([0, 0, 0, -31017, -2068976]\) | \(601211584/11025\) | \(60516574977600\) | \([2, 2]\) | \(294912\) | \(1.4393\) | \(\Gamma_0(N)\)-optimal |
| 70560.dy4 | 70560bt2 | \([0, 0, 0, -147, -6001814]\) | \(-8/354375\) | \(-15561404994240000\) | \([2]\) | \(589824\) | \(1.7858\) | |
| 70560.dy2 | 70560bt3 | \([0, 0, 0, -64092, 3117184]\) | \(82881856/36015\) | \(12651998608650240\) | \([2]\) | \(589824\) | \(1.7858\) | |
| 70560.dy1 | 70560bt4 | \([0, 0, 0, -494067, -133667786]\) | \(303735479048/105\) | \(4610786664960\) | \([2]\) | \(589824\) | \(1.7858\) |
Rank
sage: E.rank()
The elliptic curves in class 70560bt have rank \(0\).
Complex multiplication
The elliptic curves in class 70560bt do not have complex multiplication.Modular form 70560.2.a.bt
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
