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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7488.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7488.p1 | 7488q3 | \([0, 0, 0, -134796, 19048624]\) | \(11339065490696/351\) | \(8384643072\) | \([2]\) | \(24576\) | \(1.4086\) | |
7488.p2 | 7488q2 | \([0, 0, 0, -8436, 296800]\) | \(22235451328/123201\) | \(367876214784\) | \([2, 2]\) | \(12288\) | \(1.0620\) | |
7488.p3 | 7488q4 | \([0, 0, 0, -3756, 624400]\) | \(-245314376/6908733\) | \(-165034929586176\) | \([2]\) | \(24576\) | \(1.4086\) | |
7488.p4 | 7488q1 | \([0, 0, 0, -831, -1316]\) | \(1360251712/771147\) | \(35978634432\) | \([2]\) | \(6144\) | \(0.71545\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.p have rank \(0\).
Complex multiplication
The elliptic curves in class 7488.p do not have complex multiplication.Modular form 7488.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.