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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 51842g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51842.l2 | 51842g1 | \([1, 1, 0, 24, -748]\) | \(23/4\) | \(-248945284\) | \([]\) | \(28800\) | \(0.29033\) | \(\Gamma_0(N)\)-optimal |
51842.l1 | 51842g2 | \([1, 1, 0, -5611, -164163]\) | \(-313994137/64\) | \(-3983124544\) | \([]\) | \(86400\) | \(0.83963\) |
Rank
sage: E.rank()
The elliptic curves in class 51842g have rank \(1\).
Complex multiplication
The elliptic curves in class 51842g do not have complex multiplication.Modular form 51842.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.