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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 235200.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.co1 | 235200co3 | \([0, -1, 0, -500094001633, 136121307995711137]\) | \(229625675762164624948320008/9568125\) | \(576348333120000000000\) | \([2]\) | \(990904320\) | \(4.8842\) | |
| 235200.co2 | 235200co2 | \([0, -1, 0, -31255876633, 2126903032586137]\) | \(448487713888272974160064/91549016015625\) | \(689321611854225000000000000\) | \([2, 2]\) | \(495452160\) | \(4.5377\) | |
| 235200.co3 | 235200co4 | \([0, -1, 0, -31148713633, 2142211374299137]\) | \(-55486311952875723077768/801237030029296875\) | \(-48263544497109375000000000000000\) | \([2]\) | \(990904320\) | \(4.8842\) | |
| 235200.co4 | 235200co1 | \([0, -1, 0, -1960191508, 32993938276762]\) | \(7079962908642659949376/100085966990454375\) | \(11775013930459966764375000000\) | \([2]\) | \(247726080\) | \(4.1911\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.co have rank \(1\).
Complex multiplication
The elliptic curves in class 235200.co do not have complex multiplication.Modular form 235200.2.a.co
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.
