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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 87360dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.k3 | 87360dv1 | \([0, -1, 0, -1316, -17934]\) | \(3941317078336/2340975\) | \(149822400\) | \([2]\) | \(49152\) | \(0.51309\) | \(\Gamma_0(N)\)-optimal |
| 87360.k2 | 87360dv2 | \([0, -1, 0, -1561, -10535]\) | \(102766285504/46580625\) | \(190794240000\) | \([2, 2]\) | \(98304\) | \(0.85966\) | |
| 87360.k4 | 87360dv3 | \([0, -1, 0, 5439, -84735]\) | \(542939080312/404852175\) | \(-13266196070400\) | \([2]\) | \(196608\) | \(1.2062\) | |
| 87360.k1 | 87360dv4 | \([0, -1, 0, -12481, 533281]\) | \(6562309703048/106640625\) | \(3494400000000\) | \([2]\) | \(196608\) | \(1.2062\) |
Rank
sage: E.rank()
The elliptic curves in class 87360dv have rank \(2\).
Complex multiplication
The elliptic curves in class 87360dv do not have complex multiplication.Modular form 87360.2.a.dv
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
