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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 3312.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3312.l1 | 3312k2 | \([0, 0, 0, -39, 18]\) | \(949104/529\) | \(3656448\) | \([2]\) | \(384\) | \(-0.050348\) | |
| 3312.l2 | 3312k1 | \([0, 0, 0, -24, -45]\) | \(3538944/23\) | \(9936\) | \([2]\) | \(192\) | \(-0.39692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3312.l have rank \(1\).
Complex multiplication
The elliptic curves in class 3312.l do not have complex multiplication.Modular form 3312.2.a.l
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.
