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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 10080b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10080.g2 | 10080b1 | \([0, 0, 0, -33, -68]\) | \(2299968/175\) | \(302400\) | \([2]\) | \(1024\) | \(-0.20345\) | \(\Gamma_0(N)\)-optimal |
10080.g1 | 10080b2 | \([0, 0, 0, -108, 352]\) | \(1259712/245\) | \(27095040\) | \([2]\) | \(2048\) | \(0.14313\) |
Rank
sage: E.rank()
The elliptic curves in class 10080b have rank \(1\).
Complex multiplication
The elliptic curves in class 10080b do not have complex multiplication.Modular form 10080.2.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.