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SageMath
E = EllipticCurve("ip1")
E.isogeny_class()
Elliptic curves in class 235950.ip
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.ip1 | 235950ip2 | \([1, 0, 0, -139213, 17898167]\) | \(10779215329/1232010\) | \(34102826056406250\) | \([2]\) | \(2949120\) | \(1.9046\) | |
235950.ip2 | 235950ip1 | \([1, 0, 0, 12037, 1411917]\) | \(6967871/35100\) | \(-971590485937500\) | \([2]\) | \(1474560\) | \(1.5580\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.ip have rank \(0\).
Complex multiplication
The elliptic curves in class 235950.ip do not have complex multiplication.Modular form 235950.2.a.ip
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.