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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 11760bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11760.co4 | 11760bf1 | \([0, 1, 0, 180, -372]\) | \(21296/15\) | \(-451772160\) | \([2]\) | \(4608\) | \(0.34921\) | \(\Gamma_0(N)\)-optimal |
11760.co3 | 11760bf2 | \([0, 1, 0, -800, -3900]\) | \(470596/225\) | \(27106329600\) | \([2, 2]\) | \(9216\) | \(0.69578\) | |
11760.co1 | 11760bf3 | \([0, 1, 0, -10600, -423340]\) | \(546718898/405\) | \(97582786560\) | \([2]\) | \(18432\) | \(1.0424\) | |
11760.co2 | 11760bf4 | \([0, 1, 0, -6680, 205428]\) | \(136835858/1875\) | \(451772160000\) | \([2]\) | \(18432\) | \(1.0424\) |
Rank
sage: E.rank()
The elliptic curves in class 11760bf have rank \(0\).
Complex multiplication
The elliptic curves in class 11760bf do not have complex multiplication.Modular form 11760.2.a.bf
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.