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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 178695e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 178695.k2 | 178695e1 | \([1, -1, 1, -19562, -828264]\) | \(24137569/5225\) | \(179198936876025\) | \([2]\) | \(552960\) | \(1.4489\) | \(\Gamma_0(N)\)-optimal |
| 178695.k1 | 178695e2 | \([1, -1, 1, -100787, 11615406]\) | \(3301293169/218405\) | \(7490515561417845\) | \([2]\) | \(1105920\) | \(1.7955\) |
Rank
sage: E.rank()
The elliptic curves in class 178695e have rank \(1\).
Complex multiplication
The elliptic curves in class 178695e do not have complex multiplication.Modular form 178695.2.a.e
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.
