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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 14490.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.i1 | 14490a2 | \([1, -1, 0, -25095, -1523875]\) | \(64733826967442667/20736800\) | \(559893600\) | \([2]\) | \(25600\) | \(1.0391\) | |
14490.i2 | 14490a1 | \([1, -1, 0, -1575, -23299]\) | \(16008724040427/282741760\) | \(7634027520\) | \([2]\) | \(12800\) | \(0.69253\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14490.i have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.i do not have complex multiplication.Modular form 14490.2.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.