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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 40656.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.v1 | 40656bf2 | \([0, -1, 0, -875527968, 9829953052416]\) | \(10228636028672744397625/167006381634183168\) | \(1211850721092547245200375808\) | \([2]\) | \(23961600\) | \(3.9960\) | |
| 40656.v2 | 40656bf1 | \([0, -1, 0, -3243808, 430916771584]\) | \(-520203426765625/11054534935707648\) | \(-80215175025611475347570688\) | \([2]\) | \(11980800\) | \(3.6495\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40656.v have rank \(1\).
Complex multiplication
The elliptic curves in class 40656.v do not have complex multiplication.Modular form 40656.2.a.v
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.
