Properties

Label 377520ha
Number of curves $6$
Conductor $377520$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("377520.ha1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 377520ha

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
377520.ha6 377520ha1 [0, 1, 0, 29000, 770900] [2] 1966080 \(\Gamma_0(N)\)-optimal
377520.ha5 377520ha2 [0, 1, 0, -125880, 6284628] [2, 2] 3932160  
377520.ha2 377520ha3 [0, 1, 0, -1635960, 804210900] [2] 7864320  
377520.ha3 377520ha4 [0, 1, 0, -1093880, -436284972] [2, 2] 7864320  
377520.ha4 377520ha5 [0, 1, 0, -222680, -1111290732] [2] 15728640  
377520.ha1 377520ha6 [0, 1, 0, -17453080, -28070245612] [2] 15728640  

Rank

sage: E.rank()
 

The elliptic curves in class 377520ha have rank \(1\).

Modular form 377520.2.a.ha

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.