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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 253704.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253704.l1 | 253704l1 | \([0, -1, 0, -8008, -78980]\) | \(62500/33\) | \(29990524388352\) | \([2]\) | \(491520\) | \(1.2775\) | \(\Gamma_0(N)\)-optimal |
253704.l2 | 253704l2 | \([0, -1, 0, 30432, -647892]\) | \(1714750/1089\) | \(-1979374609631232\) | \([2]\) | \(983040\) | \(1.6241\) |
Rank
sage: E.rank()
The elliptic curves in class 253704.l have rank \(1\).
Complex multiplication
The elliptic curves in class 253704.l do not have complex multiplication.Modular form 253704.2.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.