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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 161874b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161874.bh1 | 161874b1 | \([1, -1, 1, -12002, 324285]\) | \(1771561/612\) | \(66045915805572\) | \([2]\) | \(760320\) | \(1.3535\) | \(\Gamma_0(N)\)-optimal |
161874.bh2 | 161874b2 | \([1, -1, 1, 35608, 2228685]\) | \(46268279/46818\) | \(-5052512559126258\) | \([2]\) | \(1520640\) | \(1.7001\) |
Rank
sage: E.rank()
The elliptic curves in class 161874b have rank \(0\).
Complex multiplication
The elliptic curves in class 161874b do not have complex multiplication.Modular form 161874.2.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.