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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 140777.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140777.g1 | 140777g3 | \([1, -1, 0, -750983, 250679456]\) | \(82483294977/17\) | \(9653777284697\) | \([2]\) | \(663552\) | \(1.8788\) | |
| 140777.g2 | 140777g2 | \([1, -1, 0, -47098, 3897375]\) | \(20346417/289\) | \(164114213839849\) | \([2, 2]\) | \(331776\) | \(1.5322\) | |
| 140777.g3 | 140777g1 | \([1, -1, 0, -5693, -69224]\) | \(35937/17\) | \(9653777284697\) | \([2]\) | \(165888\) | \(1.1856\) | \(\Gamma_0(N)\)-optimal |
| 140777.g4 | 140777g4 | \([1, -1, 0, -5693, 10480770]\) | \(-35937/83521\) | \(-47429007799716361\) | \([2]\) | \(663552\) | \(1.8788\) |
Rank
sage: E.rank()
The elliptic curves in class 140777.g have rank \(0\).
Complex multiplication
The elliptic curves in class 140777.g do not have complex multiplication.Modular form 140777.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
