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Properties

Label 309738.g
Number of curves $2$
Conductor $309738$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 309738.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309738.g1 309738g1 \([1, 1, 0, -2084558768, -36672542088576]\) \(-21293376668673906679951249/26211168887701209984\) \(-1233127532361693488463275904\) \([]\) \(231154560\) \(4.1080\) \(\Gamma_0(N)\)-optimal
309738.g2 309738g2 \([1, 1, 0, 5903465122, 2301501327836394]\) \(483641001192506212470106511/48918776756543177755473774\) \(-2301426949953896312045866270224894\) \([]\) \(1618081920\) \(5.0810\)  

Rank

sage: E.rank()
 

The elliptic curves in class 309738.g have rank \(0\).

Complex multiplication

The elliptic curves in class 309738.g do not have complex multiplication.

Modular form 309738.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.