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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 195942p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195942.t2 | 195942p1 | \([1, 1, 1, -480035, 128694593]\) | \(-506814405937489/4048994304\) | \(-97732879393406976\) | \([]\) | \(2540160\) | \(2.0881\) | \(\Gamma_0(N)\)-optimal |
195942.t1 | 195942p2 | \([1, 1, 1, -2057975, -12611592967]\) | \(-39934705050538129/2823126576537804\) | \(-68143412536915025158476\) | \([]\) | \(17781120\) | \(3.0611\) |
Rank
sage: E.rank()
The elliptic curves in class 195942p have rank \(0\).
Complex multiplication
The elliptic curves in class 195942p do not have complex multiplication.Modular form 195942.2.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 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.