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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4650.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.i1 | 4650e2 | \([1, 1, 0, -34875, -2522625]\) | \(-300238092661681/171774906\) | \(-2683982906250\) | \([]\) | \(14000\) | \(1.3311\) | |
4650.i2 | 4650e1 | \([1, 1, 0, 375, 1125]\) | \(371694959/241056\) | \(-3766500000\) | \([]\) | \(2800\) | \(0.52634\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4650.i have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.i do not have complex multiplication.Modular form 4650.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.