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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 11830s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11830.r2 | 11830s1 | \([1, -1, 1, -3657868, 2689157007]\) | \(510408052788213/980000000\) | \(10392409385540000000\) | \([2]\) | \(419328\) | \(2.5382\) | \(\Gamma_0(N)\)-optimal |
11830.r1 | 11830s2 | \([1, -1, 1, -4888188, 724582031]\) | \(1218083778723573/683593750000\) | \(7249169493261718750000\) | \([2]\) | \(838656\) | \(2.8848\) |
Rank
sage: E.rank()
The elliptic curves in class 11830s have rank \(0\).
Complex multiplication
The elliptic curves in class 11830s do not have complex multiplication.Modular form 11830.2.a.s
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.