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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 26520.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26520.v1 | 26520c4 | \([0, 1, 0, -32696, -2286480]\) | \(1887517194957938/21849165\) | \(44747089920\) | \([2]\) | \(49152\) | \(1.1949\) | |
| 26520.v2 | 26520c2 | \([0, 1, 0, -2096, -34320]\) | \(994958062276/98903025\) | \(101276697600\) | \([2, 2]\) | \(24576\) | \(0.84829\) | |
| 26520.v3 | 26520c1 | \([0, 1, 0, -476, 3264]\) | \(46689225424/7249905\) | \(1855975680\) | \([2]\) | \(12288\) | \(0.50172\) | \(\Gamma_0(N)\)-optimal |
| 26520.v4 | 26520c3 | \([0, 1, 0, 2584, -161616]\) | \(931329171502/6107473125\) | \(-12508104960000\) | \([2]\) | \(49152\) | \(1.1949\) |
Rank
sage: E.rank()
The elliptic curves in class 26520.v have rank \(1\).
Complex multiplication
The elliptic curves in class 26520.v do not have complex multiplication.Modular form 26520.2.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.
