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Properties

Label 7406i
Number of curves $2$
Conductor $7406$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 7406i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.f2 7406i1 \([1, 0, 0, -7417, -63495]\) \(304821217/164864\) \(24405788804096\) \([2]\) \(21120\) \(1.2598\) \(\Gamma_0(N)\)-optimal
7406.f1 7406i2 \([1, 0, 0, -92057, -10745063]\) \(582810602977/829472\) \(122791624920608\) \([2]\) \(42240\) \(1.6064\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7406i have rank \(0\).

Complex multiplication

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

Modular form 7406.2.a.i

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