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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 235950l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.l2 | 235950l1 | \([1, 1, 0, -2103950, 648616500]\) | \(223648543/89856\) | \(413819819770500000000\) | \([2]\) | \(10137600\) | \(2.6540\) | \(\Gamma_0(N)\)-optimal |
235950.l1 | 235950l2 | \([1, 1, 0, -15413950, -22843533500]\) | \(87943022623/1971216\) | \(9078172296215343750000\) | \([2]\) | \(20275200\) | \(3.0006\) |
Rank
sage: E.rank()
The elliptic curves in class 235950l have rank \(1\).
Complex multiplication
The elliptic curves in class 235950l do not have complex multiplication.Modular form 235950.2.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.