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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 2790w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.t2 | 2790w1 | \([1, -1, 1, 20137, -4873233]\) | \(1238798620042199/14760960000000\) | \(-10760739840000000\) | \([2]\) | \(21504\) | \(1.7571\) | \(\Gamma_0(N)\)-optimal |
2790.t1 | 2790w2 | \([1, -1, 1, -336983, -70154769]\) | \(5805223604235668521/435937500000000\) | \(317798437500000000\) | \([2]\) | \(43008\) | \(2.1037\) |
Rank
sage: E.rank()
The elliptic curves in class 2790w have rank \(0\).
Complex multiplication
The elliptic curves in class 2790w do not have complex multiplication.Modular form 2790.2.a.w
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.