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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 286650.ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.ea1 | 286650ea2 | \([1, -1, 0, -1415496977442, -648025624543090284]\) | \(682371118085879605963267423/216558834602980147200\) | \(99541875715267445578376294400000000\) | \([2]\) | \(4830658560\) | \(5.6907\) | |
| 286650.ea2 | 286650ea1 | \([1, -1, 0, -100484369442, -7197625450354284]\) | \(244112114391139785383263/92579080750403420160\) | \(42554234126653118633811640320000000\) | \([2]\) | \(2415329280\) | \(5.3441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.ea have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.ea do not have complex multiplication.Modular form 286650.2.a.ea
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
