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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 334620.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334620.z1 | 334620z1 | \([0, 0, 0, -367068, 75596573]\) | \(97152876544/12371645\) | \(696522378512909520\) | \([2]\) | \(4257792\) | \(2.1528\) | \(\Gamma_0(N)\)-optimal |
| 334620.z2 | 334620z2 | \([0, 0, 0, 553137, 393803462]\) | \(20777545136/86397025\) | \(-77826302128054022400\) | \([2]\) | \(8515584\) | \(2.4994\) |
Rank
sage: E.rank()
The elliptic curves in class 334620.z have rank \(0\).
Complex multiplication
The elliptic curves in class 334620.z do not have complex multiplication.Modular form 334620.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
