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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 9360.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9360.b1 | 9360o4 | \([0, 0, 0, -74883, 7887202]\) | \(31103978031362/195\) | \(291133440\) | \([2]\) | \(24576\) | \(1.2297\) | |
9360.b2 | 9360o3 | \([0, 0, 0, -6483, 19762]\) | \(20183398562/11567205\) | \(17269744527360\) | \([2]\) | \(24576\) | \(1.2297\) | |
9360.b3 | 9360o2 | \([0, 0, 0, -4683, 123082]\) | \(15214885924/38025\) | \(28385510400\) | \([2, 2]\) | \(12288\) | \(0.88311\) | |
9360.b4 | 9360o1 | \([0, 0, 0, -183, 3382]\) | \(-3631696/24375\) | \(-4548960000\) | \([2]\) | \(6144\) | \(0.53654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9360.b have rank \(1\).
Complex multiplication
The elliptic curves in class 9360.b do not have complex multiplication.Modular form 9360.2.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.