Properties

Label 374850ir
Number of curves $6$
Conductor $374850$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("374850.ir1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 374850ir

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
374850.ir5 374850ir1 [1, -1, 1, -774440330, 8285076708297] [2] 188743680 \(\Gamma_0(N)\)-optimal
374850.ir4 374850ir2 [1, -1, 1, -1000232330, 3060249828297] [2, 2] 377487360  
374850.ir6 374850ir3 [1, -1, 1, 3857823670, 24066483972297] [2] 754974720  
374850.ir2 374850ir4 [1, -1, 1, -9470960330, -352337614139703] [2, 2] 754974720  
374850.ir3 374850ir5 [1, -1, 1, -3225959330, -810046227431703] [2] 1509949440  
374850.ir1 374850ir6 [1, -1, 1, -151247609330, -22640193943535703] [2] 1509949440  

Rank

sage: E.rank()
 

The elliptic curves in class 374850ir have rank \(0\).

Modular form 374850.2.a.ir

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.