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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 18515.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18515.o1 | 18515i3 | \([0, 1, 1, -69475, 7350156]\) | \(-250523582464/13671875\) | \(-2023928169921875\) | \([]\) | \(71280\) | \(1.6952\) | |
18515.o2 | 18515i1 | \([0, 1, 1, -705, -8234]\) | \(-262144/35\) | \(-5181256115\) | \([]\) | \(7920\) | \(0.59660\) | \(\Gamma_0(N)\)-optimal |
18515.o3 | 18515i2 | \([0, 1, 1, 4585, 21919]\) | \(71991296/42875\) | \(-6347038740875\) | \([]\) | \(23760\) | \(1.1459\) |
Rank
sage: E.rank()
The elliptic curves in class 18515.o have rank \(1\).
Complex multiplication
The elliptic curves in class 18515.o do not have complex multiplication.Modular form 18515.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.