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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3136.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3136.d1 | 3136m2 | \([0, 1, 0, -289, 1791]\) | \(238328\) | \(11239424\) | \([2]\) | \(1024\) | \(0.20753\) | |
| 3136.d2 | 3136m1 | \([0, 1, 0, -9, 55]\) | \(-64\) | \(-1404928\) | \([2]\) | \(512\) | \(-0.13904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3136.d have rank \(2\).
Complex multiplication
The elliptic curves in class 3136.d do not have complex multiplication.Modular form 3136.2.a.d
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.
