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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 10350.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.r1 | 10350k2 | \([1, -1, 0, -393417, 83337741]\) | \(591202341974089/79350000000\) | \(903846093750000000\) | \([2]\) | \(172032\) | \(2.1729\) | |
10350.r2 | 10350k1 | \([1, -1, 0, 38583, 6873741]\) | \(557644990391/2119680000\) | \(-24144480000000000\) | \([2]\) | \(86016\) | \(1.8264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10350.r have rank \(0\).
Complex multiplication
The elliptic curves in class 10350.r do not have complex multiplication.Modular form 10350.2.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.