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Properties

Label 40898s
Number of curves $2$
Conductor $40898$
CM no
Rank $0$
Graph

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

Elliptic curves in class 40898s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40898.h2 40898s1 \([1, 0, 1, 503, 1692]\) \(24167/16\) \(-9344702224\) \([]\) \(32832\) \(0.60196\) \(\Gamma_0(N)\)-optimal
40898.h1 40898s2 \([1, 0, 1, -8792, 325158]\) \(-128667913/4096\) \(-2392243769344\) \([]\) \(98496\) \(1.1513\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40898s have rank \(0\).

Complex multiplication

The elliptic curves in class 40898s do not have complex multiplication.

Modular form 40898.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 3 q^{5} + 2 q^{6} + 2 q^{7} - q^{8} + q^{9} - 3 q^{10} - 2 q^{12} - 2 q^{14} - 6 q^{15} + q^{16} - 3 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.