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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 302016.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.d1 | 302016d2 | \([0, -1, 0, -2021345, 1106318721]\) | \(2955297238/1521\) | \(470081658946977792\) | \([2]\) | \(9191424\) | \(2.3423\) | |
| 302016.d2 | 302016d1 | \([0, -1, 0, -104705, 23417121]\) | \(-821516/1053\) | \(-162720574250876928\) | \([2]\) | \(4595712\) | \(1.9957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.d have rank \(0\).
Complex multiplication
The elliptic curves in class 302016.d do not have complex multiplication.Modular form 302016.2.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.
