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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 64974w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64974.y2 | 64974w1 | \([1, 0, 1, 1469190, -3662344724]\) | \(8691118430696801/148627738838592\) | \(-5997665362391178001344\) | \([2]\) | \(4666368\) | \(2.8593\) | \(\Gamma_0(N)\)-optimal |
64974.y1 | 64974w2 | \([1, 0, 1, -28536450, -55296050036]\) | \(63685588278222463519/4124615136744024\) | \(166443098254419604094568\) | \([2]\) | \(9332736\) | \(3.2059\) |
Rank
sage: E.rank()
The elliptic curves in class 64974w have rank \(0\).
Complex multiplication
The elliptic curves in class 64974w do not have complex multiplication.Modular form 64974.2.a.w
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.