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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 294b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
294.f2 | 294b1 | \([1, 0, 0, -1, -1]\) | \(-2401/6\) | \(-294\) | \([]\) | \(12\) | \(-0.83848\) | \(\Gamma_0(N)\)-optimal |
294.f1 | 294b2 | \([1, 0, 0, -141, 657]\) | \(-6329617441/279936\) | \(-13716864\) | \([7]\) | \(84\) | \(0.13448\) |
Rank
sage: E.rank()
The elliptic curves in class 294b have rank \(0\).
Complex multiplication
The elliptic curves in class 294b do not have complex multiplication.Modular form 294.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.