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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 57498.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57498.d1 | 57498d2 | \([1, 1, 0, -27062420, 35835135504]\) | \(16865845211125/5489031744\) | \(713364115240645707924288\) | \([2]\) | \(6905088\) | \(3.2803\) | |
| 57498.d2 | 57498d1 | \([1, 1, 0, -10853460, -13346090928]\) | \(1087959899125/37933056\) | \(4929845953504084365312\) | \([2]\) | \(3452544\) | \(2.9337\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57498.d have rank \(0\).
Complex multiplication
The elliptic curves in class 57498.d do not have complex multiplication.Modular form 57498.2.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.
