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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 309168o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309168.o2 | 309168o1 | \([0, 0, 0, -598971, 175469546]\) | \(7958910549046393/151342682688\) | \(451906829023444992\) | \([2]\) | \(3981312\) | \(2.1811\) | \(\Gamma_0(N)\)-optimal |
309168.o1 | 309168o2 | \([0, 0, 0, -1249851, -273767830]\) | \(72312097990757113/31003988313096\) | \(92577413039091646464\) | \([2]\) | \(7962624\) | \(2.5277\) |
Rank
sage: E.rank()
The elliptic curves in class 309168o have rank \(0\).
Complex multiplication
The elliptic curves in class 309168o do not have complex multiplication.Modular form 309168.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.