Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2312.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2312.a1 | 2312d2 | \([0, 1, 0, -13968, 604192]\) | \(6097250/289\) | \(14286351239168\) | \([2]\) | \(4608\) | \(1.2848\) | |
| 2312.a2 | 2312d1 | \([0, 1, 0, -2408, -33920]\) | \(62500/17\) | \(420186801152\) | \([2]\) | \(2304\) | \(0.93819\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2312.a have rank \(0\).
Complex multiplication
The elliptic curves in class 2312.a do not have complex multiplication.Modular form 2312.2.a.a
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.
