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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 349830v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
349830.v2 | 349830v1 | \([1, -1, 0, 45345, 491893325]\) | \(108531333/1100320000\) | \(-104537091647795040000\) | \([2]\) | \(11354112\) | \(2.5202\) | \(\Gamma_0(N)\)-optimal |
349830.v1 | 349830v2 | \([1, -1, 0, -9080655, 10335196925]\) | \(871613323820667/18917251600\) | \(1797253948154716225200\) | \([2]\) | \(22708224\) | \(2.8668\) |
Rank
sage: E.rank()
The elliptic curves in class 349830v have rank \(1\).
Complex multiplication
The elliptic curves in class 349830v do not have complex multiplication.Modular form 349830.2.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.