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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 7350o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.n2 | 7350o1 | \([1, 1, 0, -181325, 22525875]\) | \(5975305/1458\) | \(160878481657031250\) | \([]\) | \(90720\) | \(2.0123\) | \(\Gamma_0(N)\)-optimal |
7350.n1 | 7350o2 | \([1, 1, 0, -13686950, 19484131500]\) | \(2569823930905/72\) | \(7944616378125000\) | \([]\) | \(272160\) | \(2.5616\) |
Rank
sage: E.rank()
The elliptic curves in class 7350o have rank \(1\).
Complex multiplication
The elliptic curves in class 7350o do not have complex multiplication.Modular form 7350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.