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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 185900.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185900.o1 | 185900m2 | \([0, 0, 0, -1246375, 535518750]\) | \(88723728/11\) | \(26547449500000000\) | \([2]\) | \(1843200\) | \(2.1745\) | |
185900.o2 | 185900m1 | \([0, 0, 0, -84500, 6865625]\) | \(442368/121\) | \(18251371531250000\) | \([2]\) | \(921600\) | \(1.8280\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185900.o have rank \(0\).
Complex multiplication
The elliptic curves in class 185900.o do not have complex multiplication.Modular form 185900.2.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.