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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 56355.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56355.n1 | 56355x4 | \([1, 0, 0, -302300, -63992355]\) | \(126574061279329/16286595\) | \(393118810587555\) | \([2]\) | \(516096\) | \(1.8216\) | |
| 56355.n2 | 56355x2 | \([1, 0, 0, -20525, -818400]\) | \(39616946929/10989225\) | \(265253176694025\) | \([2, 2]\) | \(258048\) | \(1.4750\) | |
| 56355.n3 | 56355x1 | \([1, 0, 0, -7520, 240207]\) | \(1948441249/89505\) | \(2160433113345\) | \([4]\) | \(129024\) | \(1.1284\) | \(\Gamma_0(N)\)-optimal |
| 56355.n4 | 56355x3 | \([1, 0, 0, 53170, -5343273]\) | \(688699320191/910381875\) | \(-21974405324161875\) | \([2]\) | \(516096\) | \(1.8216\) |
Rank
sage: E.rank()
The elliptic curves in class 56355.n have rank \(0\).
Complex multiplication
The elliptic curves in class 56355.n do not have complex multiplication.Modular form 56355.2.a.n
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.
