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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2898.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2898.s1 | 2898q2 | \([1, -1, 1, -2144, -37547]\) | \(1494447319737/5411854\) | \(3945241566\) | \([2]\) | \(3072\) | \(0.70231\) | |
2898.s2 | 2898q1 | \([1, -1, 1, -74, -1115]\) | \(-60698457/725788\) | \(-529099452\) | \([2]\) | \(1536\) | \(0.35574\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2898.s have rank \(0\).
Complex multiplication
The elliptic curves in class 2898.s do not have complex multiplication.Modular form 2898.2.a.s
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.