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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 372810.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372810.d1 | 372810d4 | \([1, 1, 0, -1497748, -609393272]\) | \(15393836938735081/2275690697640\) | \(54929641236943637160\) | \([2]\) | \(14929920\) | \(2.5124\) | |
| 372810.d2 | 372810d3 | \([1, 1, 0, -1439948, -665655792]\) | \(13679527032530281/381633600\) | \(9211707352718400\) | \([2]\) | \(7464960\) | \(2.1658\) | |
| 372810.d3 | 372810d2 | \([1, 1, 0, -392323, 94320283]\) | \(276670733768281/336980250\) | \(8133884036012250\) | \([2]\) | \(4976640\) | \(1.9631\) | |
| 372810.d4 | 372810d1 | \([1, 1, 0, -31073, 612033]\) | \(137467988281/72562500\) | \(1751482350562500\) | \([2]\) | \(2488320\) | \(1.6165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372810.d have rank \(0\).
Complex multiplication
The elliptic curves in class 372810.d do not have complex multiplication.Modular form 372810.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
