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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 9295.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9295.b1 | 9295c4 | \([1, -1, 1, -10003, 387456]\) | \(22930509321/6875\) | \(33184311875\) | \([2]\) | \(9216\) | \(0.99681\) | |
9295.b2 | 9295c3 | \([1, -1, 1, -4933, -129008]\) | \(2749884201/73205\) | \(353346552845\) | \([2]\) | \(9216\) | \(0.99681\) | |
9295.b3 | 9295c2 | \([1, -1, 1, -708, 4502]\) | \(8120601/3025\) | \(14601097225\) | \([2, 2]\) | \(4608\) | \(0.65024\) | |
9295.b4 | 9295c1 | \([1, -1, 1, 137, 446]\) | \(59319/55\) | \(-265474495\) | \([2]\) | \(2304\) | \(0.30366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9295.b have rank \(0\).
Complex multiplication
The elliptic curves in class 9295.b do not have complex multiplication.Modular form 9295.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.