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SageMath
E = EllipticCurve("ir1")
E.isogeny_class()
Elliptic curves in class 418950.ir
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.ir1 | 418950ir2 | \([1, -1, 0, -17844192, 29017219216]\) | \(468898230633769/5540400\) | \(7424665887318750000\) | \([2]\) | \(26542080\) | \(2.7710\) | \(\Gamma_0(N)\)-optimal* |
418950.ir2 | 418950ir1 | \([1, -1, 0, -1086192, 478345216]\) | \(-105756712489/12476160\) | \(-16719247627740000000\) | \([2]\) | \(13271040\) | \(2.4244\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950.ir have rank \(0\).
Complex multiplication
The elliptic curves in class 418950.ir do not have complex multiplication.Modular form 418950.2.a.ir
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.