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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2850.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2850.i1 | 2850m2 | \([1, 0, 1, -63951, 6219298]\) | \(14809006736693/34656\) | \(67687500000\) | \([2]\) | \(9600\) | \(1.3206\) | |
2850.i2 | 2850m1 | \([1, 0, 1, -3951, 99298]\) | \(-3491055413/175104\) | \(-342000000000\) | \([2]\) | \(4800\) | \(0.97407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2850.i have rank \(1\).
Complex multiplication
The elliptic curves in class 2850.i do not have complex multiplication.Modular form 2850.2.a.i
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.