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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 379050i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.i2 | 379050i1 | \([1, 1, 0, -631781775, -6039445606875]\) | \(105093573726037969/1444738498560\) | \(383387615125835120640000000\) | \([]\) | \(248209920\) | \(3.9068\) | \(\Gamma_0(N)\)-optimal |
379050.i1 | 379050i2 | \([1, 1, 0, -51004277775, -4433636652694875]\) | \(55296123367985268658129/148176000\) | \(39321194330675250000000\) | \([]\) | \(744629760\) | \(4.4561\) |
Rank
sage: E.rank()
The elliptic curves in class 379050i have rank \(1\).
Complex multiplication
The elliptic curves in class 379050i do not have complex multiplication.Modular form 379050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.