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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 388080.ei
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.ei1 | 388080ei4 | \([0, 0, 0, -21102651003, -1175641822364758]\) | \(2958414657792917260183849/12401051653985258880\) | \(4356465036013362566424184750080\) | \([2]\) | \(924844032\) | \(4.7338\) | |
| 388080.ei2 | 388080ei2 | \([0, 0, 0, -1978068603, 1923739583402]\) | \(2436531580079063806249/1405478914998681600\) | \(493741976316828225315117465600\) | \([2, 2]\) | \(462422016\) | \(4.3872\) | |
| 388080.ei3 | 388080ei1 | \([0, 0, 0, -1400041083, 20112993977258]\) | \(863913648706111516969/2486234429521920\) | \(873409261226979175925022720\) | \([2]\) | \(231211008\) | \(4.0406\) | \(\Gamma_0(N)\)-optimal |
| 388080.ei4 | 388080ei3 | \([0, 0, 0, 7898073477, 15377020324778]\) | \(155099895405729262880471/90047655797243760000\) | \(-31633564233206824086138716160000\) | \([2]\) | \(924844032\) | \(4.7338\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.ei have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.ei do not have complex multiplication.Modular form 388080.2.a.ei
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.
