Properties

Label 372810.i
Number of curves $2$
Conductor $372810$
CM no
Rank $1$
Graph

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

Elliptic curves in class 372810.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372810.i1 372810i2 \([1, 1, 0, -68643, -6729723]\) \(1481933914201/53916840\) \(1301421445761960\) \([2]\) \(2838528\) \(1.6699\)  
372810.i2 372810i1 \([1, 1, 0, -10843, 287197]\) \(5841725401/1857600\) \(44837948174400\) \([2]\) \(1419264\) \(1.3233\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 372810.i have rank \(1\).

Complex multiplication

The elliptic curves in class 372810.i do not have complex multiplication.

Modular form 372810.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} + 2q^{11} - q^{12} - 2q^{13} - 2q^{14} + q^{15} + q^{16} - q^{18} - 6q^{19} + O(q^{20})\)  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.