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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 179520.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.g1 | 179520di4 | \([0, -1, 0, -13238721, -18535769055]\) | \(7830903984792920127368/66413740305825\) | \(2176245442341273600\) | \([2]\) | \(7864320\) | \(2.6873\) | |
| 179520.g2 | 179520di3 | \([0, -1, 0, -2902721, 1588953345]\) | \(82544817451565439368/14523938913535425\) | \(475920430318728806400\) | \([2]\) | \(7864320\) | \(2.6873\) | |
| 179520.g3 | 179520di2 | \([0, -1, 0, -845721, -275922855]\) | \(16332235051257866944/1405411999880625\) | \(5756567551511040000\) | \([2, 2]\) | \(3932160\) | \(2.3408\) | |
| 179520.g4 | 179520di1 | \([0, -1, 0, 57404, -19977230]\) | \(326860649870715584/2877853081640625\) | \(-184182597225000000\) | \([2]\) | \(1966080\) | \(1.9942\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179520.g have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.g do not have complex multiplication.Modular form 179520.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
