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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 28900.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28900.b1 | 28900d3 | \([0, 1, 0, -298633, -62899512]\) | \(488095744/125\) | \(754299031250000\) | \([2]\) | \(165888\) | \(1.8407\) | |
28900.b2 | 28900d4 | \([0, 1, 0, -262508, -78650012]\) | \(-20720464/15625\) | \(-1508598062500000000\) | \([2]\) | \(331776\) | \(2.1873\) | |
28900.b3 | 28900d1 | \([0, 1, 0, -9633, 246988]\) | \(16384/5\) | \(30171961250000\) | \([2]\) | \(55296\) | \(1.2914\) | \(\Gamma_0(N)\)-optimal |
28900.b4 | 28900d2 | \([0, 1, 0, 26492, 1691988]\) | \(21296/25\) | \(-2413756900000000\) | \([2]\) | \(110592\) | \(1.6379\) |
Rank
sage: E.rank()
The elliptic curves in class 28900.b have rank \(0\).
Complex multiplication
The elliptic curves in class 28900.b do not have complex multiplication.Modular form 28900.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.