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Properties

Label 10350.s
Number of curves $2$
Conductor $10350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 10350.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10350.s1 10350b2 \([1, -1, 0, -47067, -3805659]\) \(27333463470867/895491200\) \(377785350000000\) \([2]\) \(43008\) \(1.5705\)  
10350.s2 10350b1 \([1, -1, 0, 933, -205659]\) \(212776173/43335680\) \(-18282240000000\) \([2]\) \(21504\) \(1.2240\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10350.s have rank \(1\).

Complex multiplication

The elliptic curves in class 10350.s do not have complex multiplication.

Modular form 10350.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{7} - q^{8} - 2 q^{11} - 4 q^{13} - 2 q^{14} + q^{16} + 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.