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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 73920l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.bl2 | 73920l1 | \([0, -1, 0, -35761, 3060211]\) | \(-79028701534867456/16987307596875\) | \(-1087187686200000\) | \([]\) | \(480000\) | \(1.6063\) | \(\Gamma_0(N)\)-optimal |
73920.bl1 | 73920l2 | \([0, -1, 0, -107161, -255232229]\) | \(-2126464142970105856/438611057788643355\) | \(-28071107698473174720\) | \([]\) | \(2400000\) | \(2.4111\) |
Rank
sage: E.rank()
The elliptic curves in class 73920l have rank \(0\).
Complex multiplication
The elliptic curves in class 73920l do not have complex multiplication.Modular form 73920.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.