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SageMath
E = EllipticCurve("je1")
E.isogeny_class()
Elliptic curves in class 178752.je
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 178752.je1 | 178752cf4 | \([0, 1, 0, -274563137, -1751193571905]\) | \(74220219816682217473/16416\) | \(506285518749696\) | \([2]\) | \(17694720\) | \(3.1141\) | |
| 178752.je2 | 178752cf2 | \([0, 1, 0, -17160257, -27366484545]\) | \(18120364883707393/269485056\) | \(8311183075795009536\) | \([2, 2]\) | \(8847360\) | \(2.7675\) | |
| 178752.je3 | 178752cf3 | \([0, 1, 0, -16658497, -29041459777]\) | \(-16576888679672833/2216253521952\) | \(-68351429339809277018112\) | \([2]\) | \(17694720\) | \(3.1141\) | |
| 178752.je4 | 178752cf1 | \([0, 1, 0, -1103937, -401500737]\) | \(4824238966273/537919488\) | \(16589963878390038528\) | \([2]\) | \(4423680\) | \(2.4210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 178752.je have rank \(1\).
Complex multiplication
The elliptic curves in class 178752.je do not have complex multiplication.Modular form 178752.2.a.je
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.
