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SageMath
E = EllipticCurve("kw1")
E.isogeny_class()
Elliptic curves in class 388080.kw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.kw1 | 388080kw1 | \([0, 0, 0, -990192, -784623476]\) | \(-4890195460096/9282994875\) | \(-203818614193057248000\) | \([]\) | \(11943936\) | \(2.5868\) | \(\Gamma_0(N)\)-optimal |
| 388080.kw2 | 388080kw2 | \([0, 0, 0, 8535408, 16625315644]\) | \(3132137615458304/7250937873795\) | \(-159202512652130482993920\) | \([]\) | \(35831808\) | \(3.1361\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.kw have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.kw do not have complex multiplication.Modular form 388080.2.a.kw
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 LMFDB 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 LMFDB labels.
