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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 418950.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.a1 | 418950a2 | \([1, -1, 0, -76617, -8170709]\) | \(-3564664705/13718\) | \(-191414327343750\) | \([]\) | \(3207600\) | \(1.5990\) | |
418950.a2 | 418950a1 | \([1, -1, 0, 2133, -59459]\) | \(76895/152\) | \(-2120934375000\) | \([]\) | \(1069200\) | \(1.0497\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950.a have rank \(0\).
Complex multiplication
The elliptic curves in class 418950.a do not have complex multiplication.Modular form 418950.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.