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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 191634l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
191634.e2 | 191634l1 | \([1, 0, 1, -548, 4322]\) | \(263374721/32832\) | \(2262814272\) | \([2]\) | \(195840\) | \(0.52466\) | \(\Gamma_0(N)\)-optimal |
191634.e1 | 191634l2 | \([1, 0, 1, -2188, -35038]\) | \(16796884481/2105352\) | \(145102965192\) | \([2]\) | \(391680\) | \(0.87124\) |
Rank
sage: E.rank()
The elliptic curves in class 191634l have rank \(2\).
Complex multiplication
The elliptic curves in class 191634l do not have complex multiplication.Modular form 191634.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.