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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2450.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.o1 | 2450q2 | \([1, 1, 0, -4575, 117125]\) | \(553463785/512\) | \(9800000000\) | \([]\) | \(3240\) | \(0.84024\) | |
2450.o2 | 2450q1 | \([1, 1, 0, -200, -1000]\) | \(46585/8\) | \(153125000\) | \([]\) | \(1080\) | \(0.29094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.o have rank \(1\).
Complex multiplication
The elliptic curves in class 2450.o do not have complex multiplication.Modular form 2450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.