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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5056v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5056.t2 | 5056v1 | \([0, -1, 0, 63, -415]\) | \(103823/316\) | \(-82837504\) | \([2]\) | \(1152\) | \(0.20268\) | \(\Gamma_0(N)\)-optimal |
| 5056.t1 | 5056v2 | \([0, -1, 0, -577, -4383]\) | \(81182737/12482\) | \(3272081408\) | \([2]\) | \(2304\) | \(0.54926\) |
Rank
sage: E.rank()
The elliptic curves in class 5056v have rank \(1\).
Complex multiplication
The elliptic curves in class 5056v do not have complex multiplication.Modular form 5056.2.a.v
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.
