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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 97020cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.cw1 | 97020cw1 | \([0, 0, 0, -990192, 784623476]\) | \(-4890195460096/9282994875\) | \(-203818614193057248000\) | \([]\) | \(2985984\) | \(2.5868\) | \(\Gamma_0(N)\)-optimal |
97020.cw2 | 97020cw2 | \([0, 0, 0, 8535408, -16625315644]\) | \(3132137615458304/7250937873795\) | \(-159202512652130482993920\) | \([]\) | \(8957952\) | \(3.1361\) |
Rank
sage: E.rank()
The elliptic curves in class 97020cw have rank \(0\).
Complex multiplication
The elliptic curves in class 97020cw do not have complex multiplication.Modular form 97020.2.a.cw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.