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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 31790.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31790.p1 | 31790t1 | \([1, 1, 1, -295, 5205]\) | \(-117649/440\) | \(-10620530360\) | \([]\) | \(20160\) | \(0.60950\) | \(\Gamma_0(N)\)-optimal |
31790.p2 | 31790t2 | \([1, 1, 1, 2595, -125423]\) | \(80062991/332750\) | \(-8031776084750\) | \([]\) | \(60480\) | \(1.1588\) |
Rank
sage: E.rank()
The elliptic curves in class 31790.p have rank \(0\).
Complex multiplication
The elliptic curves in class 31790.p do not have complex multiplication.Modular form 31790.2.a.p
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.