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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 85176c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.p1 | 85176c1 | \([0, 0, 0, -88166286, 318641202945]\) | \(49860882714802176/57967\) | \(88115480464559184\) | \([2]\) | \(3870720\) | \(2.9658\) | \(\Gamma_0(N)\)-optimal |
| 85176.p2 | 85176c2 | \([0, 0, 0, -88143471, 318814355106]\) | \(-3113886554501616/3360173089\) | \(-81724640897425635502848\) | \([2]\) | \(7741440\) | \(3.3124\) |
Rank
sage: E.rank()
The elliptic curves in class 85176c have rank \(1\).
Complex multiplication
The elliptic curves in class 85176c do not have complex multiplication.Modular form 85176.2.a.c
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.
