Properties

Label 37180.a
Number of curves $4$
Conductor $37180$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 37180.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37180.a1 37180d4 \([0, 1, 0, -1199956, -506336700]\) \(154639330142416/33275\) \(41116689785600\) \([2]\) \(466560\) \(1.9969\)  
37180.a2 37180d3 \([0, 1, 0, -75261, -7871876]\) \(610462990336/8857805\) \(684078926307920\) \([2]\) \(233280\) \(1.6504\)  
37180.a3 37180d2 \([0, 1, 0, -16956, -485900]\) \(436334416/171875\) \(212379596000000\) \([2]\) \(155520\) \(1.4476\)  
37180.a4 37180d1 \([0, 1, 0, -7661, 250264]\) \(643956736/15125\) \(1168087778000\) \([2]\) \(77760\) \(1.1010\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37180.a have rank \(1\).

Complex multiplication

The elliptic curves in class 37180.a do not have complex multiplication.

Modular form 37180.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + 4 q^{7} + q^{9} + q^{11} + 2 q^{15} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.