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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 8976.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8976.v1 | 8976y3 | \([0, 1, 0, -25380904, -49224736588]\) | \(441453577446719855661097/4354701912\) | \(17836859031552\) | \([2]\) | \(258048\) | \(2.5745\) | |
| 8976.v2 | 8976y2 | \([0, 1, 0, -1586344, -769494604]\) | \(107784459654566688937/10704361149504\) | \(43845063268368384\) | \([2, 2]\) | \(129024\) | \(2.2279\) | |
| 8976.v3 | 8976y4 | \([0, 1, 0, -1466664, -890371404]\) | \(-85183593440646799657/34223681512621656\) | \(-140180199475698302976\) | \([2]\) | \(258048\) | \(2.5745\) | |
| 8976.v4 | 8976y1 | \([0, 1, 0, -106664, -10122828]\) | \(32765849647039657/8229948198912\) | \(33709867822743552\) | \([2]\) | \(64512\) | \(1.8813\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8976.v have rank \(1\).
Complex multiplication
The elliptic curves in class 8976.v do not have complex multiplication.Modular form 8976.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
