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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 858.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
858.l1 | 858l2 | \([1, 0, 0, -7372, -243952]\) | \(44308125149913793/61165323648\) | \(61165323648\) | \([2]\) | \(2016\) | \(0.97409\) | |
858.l2 | 858l1 | \([1, 0, 0, -332, -6000]\) | \(-4047806261953/13066420224\) | \(-13066420224\) | \([2]\) | \(1008\) | \(0.62752\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 858.l have rank \(0\).
Complex multiplication
The elliptic curves in class 858.l do not have complex multiplication.Modular form 858.2.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 LMFDB 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 LMFDB labels.