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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 380880v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380880.v2 | 380880v1 | \([0, 0, 0, -46023, -4550458]\) | \(-10536048/2645\) | \(-2706427651311360\) | \([2]\) | \(1351680\) | \(1.6790\) | \(\Gamma_0(N)\)-optimal |
380880.v1 | 380880v2 | \([0, 0, 0, -776043, -263123542]\) | \(12628458252/575\) | \(2353415348966400\) | \([2]\) | \(2703360\) | \(2.0256\) |
Rank
sage: E.rank()
The elliptic curves in class 380880v have rank \(2\).
Complex multiplication
The elliptic curves in class 380880v do not have complex multiplication.Modular form 380880.2.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.