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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 24990.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.o1 | 24990k4 | \([1, 1, 0, -6266047, 6034613509]\) | \(231268521845235080809/816013464000\) | \(96003168026136000\) | \([2]\) | \(663552\) | \(2.4773\) | |
24990.o2 | 24990k3 | \([1, 1, 0, -386047, 96989509]\) | \(-54082626581000809/3358656000000\) | \(-395142519744000000\) | \([2]\) | \(331776\) | \(2.1307\) | |
24990.o3 | 24990k2 | \([1, 1, 0, -106012, 1560196]\) | \(1119971462469049/638680075740\) | \(75140072230735260\) | \([2]\) | \(221184\) | \(1.9280\) | |
24990.o4 | 24990k1 | \([1, 1, 0, 26288, 210736]\) | \(17075848639751/10028415600\) | \(-1179833066924400\) | \([2]\) | \(110592\) | \(1.5814\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24990.o have rank \(1\).
Complex multiplication
The elliptic curves in class 24990.o do not have complex multiplication.Modular form 24990.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.