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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 10830.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.r1 | 10830s2 | \([1, 1, 1, -9632751, 11474043573]\) | \(306331959547531/900000000\) | \(290418928001100000000\) | \([2]\) | \(1167360\) | \(2.7967\) | |
10830.r2 | 10830s1 | \([1, 1, 1, -853231, 15014069]\) | \(212883113611/122880000\) | \(39651864303083520000\) | \([2]\) | \(583680\) | \(2.4501\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.r have rank \(0\).
Complex multiplication
The elliptic curves in class 10830.r do not have complex multiplication.Modular form 10830.2.a.r
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.