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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 259182i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.i2 | 259182i1 | \([1, -1, 0, 1974, 170748]\) | \(17779581/275128\) | \(-13159962939816\) | \([]\) | \(648000\) | \(1.1980\) | \(\Gamma_0(N)\)-optimal |
259182.i1 | 259182i2 | \([1, -1, 0, -183156, 30231746]\) | \(-19486825371/11662\) | \(-406649685270906\) | \([]\) | \(1944000\) | \(1.7473\) |
Rank
sage: E.rank()
The elliptic curves in class 259182i have rank \(0\).
Complex multiplication
The elliptic curves in class 259182i do not have complex multiplication.Modular form 259182.2.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 Cremona 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 Cremona labels.