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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 910.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 910.g1 | 910j6 | \([1, 0, 0, -529046, -148084874]\) | \(16375858190544687071329/9025573730468750\) | \(9025573730468750\) | \([2]\) | \(10368\) | \(2.0095\) | |
| 910.g2 | 910j5 | \([1, 0, 0, -528976, -148126020]\) | \(16369358802802724130049/4976562500\) | \(4976562500\) | \([2]\) | \(5184\) | \(1.6630\) | |
| 910.g3 | 910j4 | \([1, 0, 0, -20356, 876120]\) | \(932829715460155969/206949435875000\) | \(206949435875000\) | \([6]\) | \(3456\) | \(1.4602\) | |
| 910.g4 | 910j2 | \([1, 0, 0, -19116, 1015696]\) | \(772531501373731009/15142400\) | \(15142400\) | \([6]\) | \(1152\) | \(0.91093\) | |
| 910.g5 | 910j3 | \([1, 0, 0, -6636, -196784]\) | \(32318182904349889/2067798824000\) | \(2067798824000\) | \([6]\) | \(1728\) | \(1.1137\) | |
| 910.g6 | 910j1 | \([1, 0, 0, -1196, 15760]\) | \(189208196468929/834928640\) | \(834928640\) | \([6]\) | \(576\) | \(0.56436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 910.g have rank \(0\).
Complex multiplication
The elliptic curves in class 910.g do not have complex multiplication.Modular form 910.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 6 & 18 \\ 2 & 1 & 6 & 18 & 3 & 9 \\ 3 & 6 & 1 & 3 & 2 & 6 \\ 9 & 18 & 3 & 1 & 6 & 2 \\ 6 & 3 & 2 & 6 & 1 & 3 \\ 18 & 9 & 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
