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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 163170eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 163170.g2 | 163170eh1 | \([1, -1, 0, -2015820, -1102982000]\) | \(-10562417119034929/20894462400\) | \(-1792036990428350400\) | \([2]\) | \(4423680\) | \(2.3905\) | \(\Gamma_0(N)\)-optimal |
| 163170.g1 | 163170eh2 | \([1, -1, 0, -32268420, -70544800040]\) | \(43325247696520145329/169044120\) | \(14498258450258520\) | \([2]\) | \(8847360\) | \(2.7371\) |
Rank
sage: E.rank()
The elliptic curves in class 163170eh have rank \(1\).
Complex multiplication
The elliptic curves in class 163170eh do not have complex multiplication.Modular form 163170.2.a.eh
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.
