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SageMath
E = EllipticCurve("jg1")
E.isogeny_class()
Elliptic curves in class 348480.jg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.jg1 | 348480jg3 | \([0, 0, 0, -748129932, -7876129442544]\) | \(5066026756449723/11000000\) | \(100549522041864192000000\) | \([2]\) | \(119439360\) | \(3.6606\) | |
| 348480.jg2 | 348480jg4 | \([0, 0, 0, -739766412, -8060826072816]\) | \(-4898016158612283/236328125000\) | \(-2160243637618176000000000000\) | \([2]\) | \(238878720\) | \(4.0071\) | |
| 348480.jg3 | 348480jg1 | \([0, 0, 0, -12140172, -3448695536]\) | \(15781142246787/8722841600\) | \(109374928760056106188800\) | \([2]\) | \(39813120\) | \(3.1113\) | \(\Gamma_0(N)\)-optimal |
| 348480.jg4 | 348480jg2 | \([0, 0, 0, 47333748, -27262053104]\) | \(935355271080573/566899520000\) | \(-7108302254864974479360000\) | \([2]\) | \(79626240\) | \(3.4578\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.jg have rank \(0\).
Complex multiplication
The elliptic curves in class 348480.jg do not have complex multiplication.Modular form 348480.2.a.jg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
