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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 95874.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95874.b1 | 95874a3 | \([1, 1, 0, -359965, -83275799]\) | \(8671983378625/82308\) | \(48958717904868\) | \([2]\) | \(870912\) | \(1.7892\) | |
95874.b2 | 95874a4 | \([1, 1, 0, -351555, -87341193]\) | \(-8078253774625/846825858\) | \(-503711769164234418\) | \([2]\) | \(1741824\) | \(2.1357\) | |
95874.b3 | 95874a1 | \([1, 1, 0, -6745, 13477]\) | \(57066625/32832\) | \(19529239275072\) | \([2]\) | \(290304\) | \(1.2398\) | \(\Gamma_0(N)\)-optimal |
95874.b4 | 95874a2 | \([1, 1, 0, 26895, 141309]\) | \(3616805375/2105352\) | \(-1252312468513992\) | \([2]\) | \(580608\) | \(1.5864\) |
Rank
sage: E.rank()
The elliptic curves in class 95874.b have rank \(1\).
Complex multiplication
The elliptic curves in class 95874.b do not have complex multiplication.Modular form 95874.2.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.