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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 99856g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99856.o3 | 99856g1 | \([0, 1, 0, -4645384, 3852080884]\) | \(11134383337/316\) | \(314636844829229056\) | \([]\) | \(1996800\) | \(2.4591\) | \(\Gamma_0(N)\)-optimal |
| 99856.o2 | 99856g2 | \([0, 1, 0, -8140344, -2683494316]\) | \(59914169497/31554496\) | \(31418376777267496615936\) | \([]\) | \(5990400\) | \(3.0084\) | |
| 99856.o1 | 99856g3 | \([0, 1, 0, -520900904, -4576113258316]\) | \(15698803397448457/20709376\) | \(20620040262728355414016\) | \([]\) | \(17971200\) | \(3.5577\) |
Rank
sage: E.rank()
The elliptic curves in class 99856g have rank \(1\).
Complex multiplication
The elliptic curves in class 99856g do not have complex multiplication.Modular form 99856.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
