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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 189618.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.o1 | 189618y2 | \([1, 0, 1, -30762, 2073970]\) | \(666940371553/37026\) | \(178717430034\) | \([2]\) | \(414720\) | \(1.2245\) | |
189618.o2 | 189618y1 | \([1, 0, 1, -2032, 28394]\) | \(192100033/38148\) | \(184133109732\) | \([2]\) | \(207360\) | \(0.87789\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 189618.o have rank \(0\).
Complex multiplication
The elliptic curves in class 189618.o do not have complex multiplication.Modular form 189618.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.