Properties

Label 374850la
Number of curves $4$
Conductor $374850$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("la1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 374850la

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374850.la4 374850la1 \([1, -1, 1, 10795, 116650797]\) \(103823/4386816\) \(-5878752997824000000\) \([2]\) \(9437184\) \(2.2804\) \(\Gamma_0(N)\)-optimal
374850.la3 374850la2 \([1, -1, 1, -3517205, 2494522797]\) \(3590714269297/73410624\) \(98377257197961000000\) \([2, 2]\) \(18874368\) \(2.6270\)  
374850.la1 374850la3 \([1, -1, 1, -55996205, 161295976797]\) \(14489843500598257/6246072\) \(8370333858229875000\) \([2]\) \(37748736\) \(2.9735\)  
374850.la2 374850la4 \([1, -1, 1, -7486205, -4165459203]\) \(34623662831857/14438442312\) \(19348893599726746125000\) \([2]\) \(37748736\) \(2.9735\)  

Rank

sage: E.rank()
 

The elliptic curves in class 374850la have rank \(2\).

Complex multiplication

The elliptic curves in class 374850la do not have complex multiplication.

Modular form 374850.2.a.la

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 6q^{13} + q^{16} - q^{17} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.