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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 16560b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16560.r2 | 16560b1 | \([0, 0, 0, -783, -10098]\) | \(-10536048/2645\) | \(-13327752960\) | \([2]\) | \(7680\) | \(0.66054\) | \(\Gamma_0(N)\)-optimal |
16560.r1 | 16560b2 | \([0, 0, 0, -13203, -583902]\) | \(12628458252/575\) | \(11589350400\) | \([2]\) | \(15360\) | \(1.0071\) |
Rank
sage: E.rank()
The elliptic curves in class 16560b have rank \(1\).
Complex multiplication
The elliptic curves in class 16560b do not have complex multiplication.Modular form 16560.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.