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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 39270.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39270.g1 | 39270f4 | \([1, 1, 0, -37735098, 89196418452]\) | \(5942376666521498646800152489/671118164062500000000\) | \(671118164062500000000\) | \([2]\) | \(3932160\) | \(3.0242\) | |
| 39270.g2 | 39270f3 | \([1, 1, 0, -14549178, -20428990572]\) | \(340595676265053452580100009/16918505152329026400000\) | \(16918505152329026400000\) | \([2]\) | \(3932160\) | \(3.0242\) | |
| 39270.g3 | 39270f2 | \([1, 1, 0, -2549178, 1154209428]\) | \(1831995757526953572100009/483612877440000000000\) | \(483612877440000000000\) | \([2, 2]\) | \(1966080\) | \(2.6776\) | |
| 39270.g4 | 39270f1 | \([1, 1, 0, 399942, 116709012]\) | \(7074781925189541238871/9961680037478400000\) | \(-9961680037478400000\) | \([2]\) | \(983040\) | \(2.3311\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39270.g have rank \(0\).
Complex multiplication
The elliptic curves in class 39270.g do not have complex multiplication.Modular form 39270.2.a.g
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.
