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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 612.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 612.d1 | 612a1 | \([0, 0, 0, -456, 3748]\) | \(-1517101056/17\) | \(-117504\) | \([3]\) | \(144\) | \(0.12585\) | \(\Gamma_0(N)\)-optimal |
| 612.d2 | 612a2 | \([0, 0, 0, -216, 7668]\) | \(-221184/4913\) | \(-24755860224\) | \([]\) | \(432\) | \(0.67515\) |
Rank
sage: E.rank()
The elliptic curves in class 612.d have rank \(0\).
Complex multiplication
The elliptic curves in class 612.d do not have complex multiplication.Modular form 612.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
