Properties

Label 309442.a
Number of curves $2$
Conductor $309442$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 309442.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309442.a1 309442a2 \([1, 0, 1, -581906, -160003164]\) \(24553362849625/1755162752\) \(1557713403154090112\) \([2]\) \(6773760\) \(2.2377\)  
309442.a2 309442a1 \([1, 0, 1, 33134, -10917468]\) \(4533086375/60669952\) \(-53844805726093312\) \([2]\) \(3386880\) \(1.8912\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 309442.a have rank \(2\).

Complex multiplication

The elliptic curves in class 309442.a do not have complex multiplication.

Modular form 309442.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + q^{7} - q^{8} + q^{9} - 4q^{11} - 2q^{12} - q^{14} + q^{16} - 6q^{17} - q^{18} - 6q^{19} + O(q^{20})\)  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.