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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 274890g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 274890.g4 | 274890g1 | \([1, 1, 0, -1603893, -769943187]\) | \(3878484596972846281/71498889000000\) | \(8411772791961000000\) | \([2]\) | \(7962624\) | \(2.4259\) | \(\Gamma_0(N)\)-optimal |
| 274890.g3 | 274890g2 | \([1, 1, 0, -3318893, 1163547813]\) | \(34364927331294686281/14904055767447000\) | \(1753447256984372103000\) | \([2]\) | \(15925248\) | \(2.7725\) | |
| 274890.g2 | 274890g3 | \([1, 1, 0, -14411268, 20710023888]\) | \(2813468797630571444281/52337913161318400\) | \(6157503145515948441600\) | \([2]\) | \(23887872\) | \(2.9752\) | |
| 274890.g1 | 274890g4 | \([1, 1, 0, -229540868, 1338464875728]\) | \(11368823750620983511373881/4046043507770880\) | \(476012972645736261120\) | \([2]\) | \(47775744\) | \(3.3218\) |
Rank
sage: E.rank()
The elliptic curves in class 274890g have rank \(0\).
Complex multiplication
The elliptic curves in class 274890g do not have complex multiplication.Modular form 274890.2.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 Cremona 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 Cremona labels.
