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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 35728.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35728.i1 | 35728v1 | \([0, -1, 0, -1013, -18371]\) | \(-28094464000/20657483\) | \(-84613050368\) | \([]\) | \(24192\) | \(0.79622\) | \(\Gamma_0(N)\)-optimal |
35728.i2 | 35728v2 | \([0, -1, 0, 8267, 286013]\) | \(15252992000000/17621717267\) | \(-72178553925632\) | \([]\) | \(72576\) | \(1.3455\) |
Rank
sage: E.rank()
The elliptic curves in class 35728.i have rank \(0\).
Complex multiplication
The elliptic curves in class 35728.i do not have complex multiplication.Modular form 35728.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.