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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 23232z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23232.e2 | 23232z1 | \([0, -1, 0, -253777, 56106481]\) | \(-4253392/729\) | \(-309794939439169536\) | \([]\) | \(354816\) | \(2.0826\) | \(\Gamma_0(N)\)-optimal |
| 23232.e1 | 23232z2 | \([0, -1, 0, -21336817, 37942329361]\) | \(-2527934627152/9\) | \(-3824628881965056\) | \([]\) | \(1064448\) | \(2.6319\) |
Rank
sage: E.rank()
The elliptic curves in class 23232z have rank \(0\).
Complex multiplication
The elliptic curves in class 23232z do not have complex multiplication.Modular form 23232.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
