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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 35280en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.o2 | 35280en1 | \([0, 0, 0, -501123, -160574078]\) | \(-115501303/25600\) | \(-3084677756013772800\) | \([2]\) | \(645120\) | \(2.2682\) | \(\Gamma_0(N)\)-optimal |
| 35280.o1 | 35280en2 | \([0, 0, 0, -8403843, -9376726142]\) | \(544737993463/20000\) | \(2409904496885760000\) | \([2]\) | \(1290240\) | \(2.6148\) |
Rank
sage: E.rank()
The elliptic curves in class 35280en have rank \(0\).
Complex multiplication
The elliptic curves in class 35280en do not have complex multiplication.Modular form 35280.2.a.en
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
