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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 69938q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69938.u2 | 69938q1 | \([1, 1, 1, 861, 4049]\) | \(24167/16\) | \(-46730333584\) | \([]\) | \(80640\) | \(0.73609\) | \(\Gamma_0(N)\)-optimal |
69938.u1 | 69938q2 | \([1, 1, 1, -15034, 722503]\) | \(-128667913/4096\) | \(-11962965397504\) | \([]\) | \(241920\) | \(1.2854\) |
Rank
sage: E.rank()
The elliptic curves in class 69938q have rank \(1\).
Complex multiplication
The elliptic curves in class 69938q do not have complex multiplication.Modular form 69938.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.