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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 480240.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480240.l1 | 480240l2 | \([0, 0, 0, -418923, 102644378]\) | \(73519511861296467/1390278125000\) | \(153753638400000000\) | \([2]\) | \(4718592\) | \(2.0915\) | |
480240.l2 | 480240l1 | \([0, 0, 0, -417003, 103647002]\) | \(72513278012259027/26680000\) | \(2950594560000\) | \([2]\) | \(2359296\) | \(1.7449\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 480240.l have rank \(0\).
Complex multiplication
The elliptic curves in class 480240.l do not have complex multiplication.Modular form 480240.2.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.