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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 286110p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.p2 | 286110p1 | \([1, -1, 0, -135343395, 606397816341]\) | \(-76552718951074800841217/46883277813841920\) | \(-167916069502666502307840\) | \([2]\) | \(58982400\) | \(3.3994\) | \(\Gamma_0(N)\)-optimal |
286110.p1 | 286110p2 | \([1, -1, 0, -2165812515, 38795867119125]\) | \(313698178215636326146617857/117552284467200\) | \(421022558345180774400\) | \([2]\) | \(117964800\) | \(3.7460\) |
Rank
sage: E.rank()
The elliptic curves in class 286110p have rank \(1\).
Complex multiplication
The elliptic curves in class 286110p do not have complex multiplication.Modular form 286110.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.