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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 7488.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7488.bl1 | 7488p4 | \([0, 0, 0, -40044, 3084208]\) | \(37159393753/1053\) | \(201231433728\) | \([2]\) | \(16384\) | \(1.2707\) | |
7488.bl2 | 7488p3 | \([0, 0, 0, -11244, -415568]\) | \(822656953/85683\) | \(16374276292608\) | \([2]\) | \(16384\) | \(1.2707\) | |
7488.bl3 | 7488p2 | \([0, 0, 0, -2604, 44080]\) | \(10218313/1521\) | \(290667626496\) | \([2, 2]\) | \(8192\) | \(0.92409\) | |
7488.bl4 | 7488p1 | \([0, 0, 0, 276, 3760]\) | \(12167/39\) | \(-7453016064\) | \([2]\) | \(4096\) | \(0.57751\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 7488.bl do not have complex multiplication.Modular form 7488.2.a.bl
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.