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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 247962i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247962.i2 | 247962i1 | \([1, 1, 0, -1556704, -502152308]\) | \(3518049774329/1119705444\) | \(132783490906090549668\) | \([2]\) | \(8077312\) | \(2.5651\) | \(\Gamma_0(N)\)-optimal |
247962.i1 | 247962i2 | \([1, 1, 0, -9859674, 11532172410]\) | \(893863401019289/32468145138\) | \(3850328385711815021586\) | \([2]\) | \(16154624\) | \(2.9117\) |
Rank
sage: E.rank()
The elliptic curves in class 247962i have rank \(1\).
Complex multiplication
The elliptic curves in class 247962i do not have complex multiplication.Modular form 247962.2.a.i
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.