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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1170g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1170.g3 | 1170g1 | \([1, -1, 0, -54, -972]\) | \(-24137569/561600\) | \(-409406400\) | \([2]\) | \(384\) | \(0.33325\) | \(\Gamma_0(N)\)-optimal |
1170.g2 | 1170g2 | \([1, -1, 0, -1854, -30132]\) | \(967068262369/4928040\) | \(3592541160\) | \([2]\) | \(768\) | \(0.67982\) | |
1170.g4 | 1170g3 | \([1, -1, 0, 486, 25920]\) | \(17394111071/411937500\) | \(-300302437500\) | \([6]\) | \(1152\) | \(0.88256\) | |
1170.g1 | 1170g4 | \([1, -1, 0, -10764, 410670]\) | \(189208196468929/10860320250\) | \(7917173462250\) | \([6]\) | \(2304\) | \(1.2291\) |
Rank
sage: E.rank()
The elliptic curves in class 1170g have rank \(0\).
Complex multiplication
The elliptic curves in class 1170g do not have complex multiplication.Modular form 1170.2.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.