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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 290400eq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290400.eq2 | 290400eq1 | \([0, 1, 0, 5042, 1234088]\) | \(64/3\) | \(-664335375000000\) | \([2]\) | \(1036800\) | \(1.5239\) | \(\Gamma_0(N)\)-optimal |
290400.eq1 | 290400eq2 | \([0, 1, 0, -146208, 20594088]\) | \(195112/9\) | \(15944049000000000\) | \([2]\) | \(2073600\) | \(1.8705\) |
Rank
sage: E.rank()
The elliptic curves in class 290400eq have rank \(1\).
Complex multiplication
The elliptic curves in class 290400eq do not have complex multiplication.Modular form 290400.2.a.eq
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.