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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 26950.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26950.p1 | 26950w2 | \([1, 1, 0, -7276525, 7551963875]\) | \(-23178622194826561/1610510\) | \(-2960545171718750\) | \([]\) | \(792000\) | \(2.4227\) | |
26950.p2 | 26950w1 | \([1, 1, 0, 12225, 2105125]\) | \(109902239/1100000\) | \(-2022092187500000\) | \([]\) | \(158400\) | \(1.6180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26950.p have rank \(1\).
Complex multiplication
The elliptic curves in class 26950.p do not have complex multiplication.Modular form 26950.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.