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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 38640.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.cg1 | 38640ct4 | \([0, 1, 0, -80816, -8869740]\) | \(14251520160844849/264449745\) | \(1083186155520\) | \([2]\) | \(122880\) | \(1.4342\) | |
| 38640.cg2 | 38640ct2 | \([0, 1, 0, -5216, -130380]\) | \(3832302404449/472410225\) | \(1934992281600\) | \([2, 2]\) | \(61440\) | \(1.0876\) | |
| 38640.cg3 | 38640ct1 | \([0, 1, 0, -1296, 15444]\) | \(58818484369/7455105\) | \(30536110080\) | \([2]\) | \(30720\) | \(0.74103\) | \(\Gamma_0(N)\)-optimal |
| 38640.cg4 | 38640ct3 | \([0, 1, 0, 7664, -661036]\) | \(12152722588271/53476250625\) | \(-219038722560000\) | \([2]\) | \(122880\) | \(1.4342\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.cg have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.cg do not have complex multiplication.Modular form 38640.2.a.cg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
