Properties

Label 79350.c
Number of curves $2$
Conductor $79350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 79350.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.c1 79350m2 \([1, 1, 0, -39080150, -17158447500]\) \(234542659463/131220000\) \(3692925816205857187500000\) \([2]\) \(16957440\) \(3.4043\)  
79350.c2 79350m1 \([1, 1, 0, 9587850, -2120035500]\) \(3463512697/2073600\) \(-58357346231401200000000\) \([2]\) \(8478720\) \(3.0577\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 79350.c have rank \(0\).

Complex multiplication

The elliptic curves in class 79350.c do not have complex multiplication.

Modular form 79350.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} + 2 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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 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.