Properties

Label 7406.c
Number of curves $2$
Conductor $7406$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7406.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.c1 7406e2 \([1, -1, 0, -467, -3735]\) \(926859375/9604\) \(116851868\) \([2]\) \(2304\) \(0.36507\)  
7406.c2 7406e1 \([1, -1, 0, -7, -147]\) \(-3375/784\) \(-9538928\) \([2]\) \(1152\) \(0.018494\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7406.c have rank \(1\).

Complex multiplication

The elliptic curves in class 7406.c do not have complex multiplication.

Modular form 7406.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} - 4 q^{11} - 2 q^{13} - q^{14} + q^{16} + 4 q^{17} + 3 q^{18} + 4 q^{19} + O(q^{20})\)  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.