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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 14651l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14651.d2 | 14651l1 | \([1, 0, 0, 832, 9295]\) | \(541343375/625807\) | \(-73625567743\) | \([2]\) | \(11520\) | \(0.77153\) | \(\Gamma_0(N)\)-optimal |
14651.d1 | 14651l2 | \([1, 0, 0, -4803, 87058]\) | \(104154702625/32188247\) | \(3786915071303\) | \([2]\) | \(23040\) | \(1.1181\) |
Rank
sage: E.rank()
The elliptic curves in class 14651l have rank \(1\).
Complex multiplication
The elliptic curves in class 14651l do not have complex multiplication.Modular form 14651.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.