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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 155298x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155298.l2 | 155298x1 | \([1, 0, 1, -6256, 188270]\) | \(27071613221109625/268992286992\) | \(268992286992\) | \([2]\) | \(253440\) | \(1.0119\) | \(\Gamma_0(N)\)-optimal |
155298.l1 | 155298x2 | \([1, 0, 1, -11116, -146098]\) | \(151884397619853625/78791770582668\) | \(78791770582668\) | \([2]\) | \(506880\) | \(1.3584\) |
Rank
sage: E.rank()
The elliptic curves in class 155298x have rank \(2\).
Complex multiplication
The elliptic curves in class 155298x do not have complex multiplication.Modular form 155298.2.a.x
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.