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SageMath
E = EllipticCurve("me1")
E.isogeny_class()
Elliptic curves in class 388080me
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.me1 | 388080me1 | \([0, 0, 0, -1715112, 864543484]\) | \(-1647408715474378752/3025\) | \(-1024531200\) | \([]\) | \(2571264\) | \(1.8754\) | \(\Gamma_0(N)\)-optimal |
| 388080.me2 | 388080me2 | \([0, 0, 0, -1710072, 869877036]\) | \(-2239956387422208/27680640625\) | \(-6834448491948000000\) | \([]\) | \(7713792\) | \(2.4248\) |
Rank
sage: E.rank()
The elliptic curves in class 388080me have rank \(1\).
Complex multiplication
The elliptic curves in class 388080me do not have complex multiplication.Modular form 388080.2.a.me
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
