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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 61347v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61347.t1 | 61347v1 | \([0, 1, 1, -1499593, 714008455]\) | \(-360448000/4563\) | \(-4721196362873846427\) | \([]\) | \(887040\) | \(2.3930\) | \(\Gamma_0(N)\)-optimal |
61347.t2 | 61347v2 | \([0, 1, 1, 5248577, 3643389052]\) | \(15454208000/14480427\) | \(-14982454368893325311283\) | \([]\) | \(2661120\) | \(2.9423\) |
Rank
sage: E.rank()
The elliptic curves in class 61347v have rank \(1\).
Complex multiplication
The elliptic curves in class 61347v do not have complex multiplication.Modular form 61347.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.