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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 31850q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31850.a2 | 31850q1 | \([1, -1, 0, -3292, -110384]\) | \(-2146689/1664\) | \(-3058874000000\) | \([]\) | \(105840\) | \(1.0945\) | \(\Gamma_0(N)\)-optimal |
31850.a1 | 31850q2 | \([1, -1, 0, -260542, 56227366]\) | \(-1064019559329/125497034\) | \(-230696883641656250\) | \([]\) | \(740880\) | \(2.0675\) |
Rank
sage: E.rank()
The elliptic curves in class 31850q have rank \(0\).
Complex multiplication
The elliptic curves in class 31850q do not have complex multiplication.Modular form 31850.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.