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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 40432o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40432.k2 | 40432o1 | \([0, 0, 0, 893, 300162]\) | \(53261199/26353376\) | \(-38967577542656\) | \([]\) | \(60480\) | \(1.2869\) | \(\Gamma_0(N)\)-optimal |
| 40432.k1 | 40432o2 | \([0, 0, 0, -1212067, -514416222]\) | \(-133179212896925841/240518168576\) | \(-355643633073913856\) | \([]\) | \(423360\) | \(2.2598\) |
Rank
sage: E.rank()
The elliptic curves in class 40432o have rank \(1\).
Complex multiplication
The elliptic curves in class 40432o do not have complex multiplication.Modular form 40432.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
