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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 82368ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82368.bt1 | 82368ea1 | \([0, 0, 0, -3326054988, 73910076508816]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-5009032378878311026743312384\) | \([]\) | \(54190080\) | \(4.2248\) | \(\Gamma_0(N)\)-optimal |
| 82368.bt2 | 82368ea2 | \([0, 0, 0, 9419379252, -4638565439867504]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-9348523820455028741568038501351424\) | \([]\) | \(379330560\) | \(5.1978\) |
Rank
sage: E.rank()
The elliptic curves in class 82368ea have rank \(0\).
Complex multiplication
The elliptic curves in class 82368ea do not have complex multiplication.Modular form 82368.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
