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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 274890q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.q2 | 274890q1 | \([1, 1, 0, -2660333, 863532573]\) | \(17698796351170126921/7497201903206400\) | \(882038306710329753600\) | \([2]\) | \(17031168\) | \(2.7158\) | \(\Gamma_0(N)\)-optimal |
274890.q1 | 274890q2 | \([1, 1, 0, -20221933, -34410697187]\) | \(7773265598236356584521/152617531058657280\) | \(17955299911519970334720\) | \([2]\) | \(34062336\) | \(3.0624\) |
Rank
sage: E.rank()
The elliptic curves in class 274890q have rank \(0\).
Complex multiplication
The elliptic curves in class 274890q do not have complex multiplication.Modular form 274890.2.a.q
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.