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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 374790l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374790.l1 | 374790l1 | \([1, 1, 0, -30957193, -66783667013]\) | \(-4003054657369/33264270\) | \(-27264336637766849280270\) | \([]\) | \(40176000\) | \(3.1314\) | \(\Gamma_0(N)\)-optimal |
374790.l2 | 374790l2 | \([1, 1, 0, 93718142, -353960833652]\) | \(111065142046871/130323843000\) | \(-106817108190844853538243000\) | \([]\) | \(120528000\) | \(3.6807\) |
Rank
sage: E.rank()
The elliptic curves in class 374790l have rank \(0\).
Complex multiplication
The elliptic curves in class 374790l do not have complex multiplication.Modular form 374790.2.a.l
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.