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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 342720.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 342720.cg1 | 342720cg4 | \([0, 0, 0, -35251788, -80560070512]\) | \(25351269426118370449/27551475\) | \(5265168865689600\) | \([2]\) | \(12582912\) | \(2.7354\) | |
| 342720.cg2 | 342720cg3 | \([0, 0, 0, -2748108, -589011568]\) | \(12010404962647729/6166198828125\) | \(1178378946662400000000\) | \([2]\) | \(12582912\) | \(2.7354\) | |
| 342720.cg3 | 342720cg2 | \([0, 0, 0, -2203788, -1258089712]\) | \(6193921595708449/6452105625\) | \(1233016586403840000\) | \([2, 2]\) | \(6291456\) | \(2.3888\) | |
| 342720.cg4 | 342720cg1 | \([0, 0, 0, -104268, -29450608]\) | \(-656008386769/1581036975\) | \(-302140871088537600\) | \([2]\) | \(3145728\) | \(2.0423\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 342720.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 342720.cg do not have complex multiplication.Modular form 342720.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
