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SageMath
E = EllipticCurve("gy1")
E.isogeny_class()
Elliptic curves in class 336336gy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 336336.gy2 | 336336gy1 | \([0, 1, 0, -56856480, -165030546444]\) | \(860833894093732321/8282804244\) | \(195578749700568858624\) | \([]\) | \(26869248\) | \(3.0551\) | \(\Gamma_0(N)\)-optimal |
| 336336.gy1 | 336336gy2 | \([0, 1, 0, -1832608640, 30187401288372]\) | \(28826282175168869972161/9077387406557184\) | \(214340943866709036566052864\) | \([]\) | \(188084736\) | \(4.0280\) |
Rank
sage: E.rank()
The elliptic curves in class 336336gy have rank \(0\).
Complex multiplication
The elliptic curves in class 336336gy do not have complex multiplication.Modular form 336336.2.a.gy
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.
