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Properties

Label 37905.m
Number of curves $4$
Conductor $37905$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 37905.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37905.m1 37905b4 \([1, 1, 0, -16534168, -25884159203]\) \(10625495353235512849/90517708575\) \(4258485346012129575\) \([2]\) \(1935360\) \(2.7430\)  
37905.m2 37905b3 \([1, 1, 0, -3628418, 2218625847]\) \(112293400033564849/19723834261425\) \(927925159526723440425\) \([2]\) \(1935360\) \(2.7430\)  
37905.m3 37905b2 \([1, 1, 0, -1056293, -385907928]\) \(2770485962938849/238901000625\) \(11239308046184675625\) \([2, 2]\) \(967680\) \(2.3965\)  
37905.m4 37905b1 \([1, 1, 0, 71832, -27841053]\) \(871257511151/7637109375\) \(-359294538840234375\) \([2]\) \(483840\) \(2.0499\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37905.m have rank \(0\).

Complex multiplication

The elliptic curves in class 37905.m do not have complex multiplication.

Modular form 37905.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - q^{7} - 3 q^{8} + q^{9} - q^{10} + q^{12} + 6 q^{13} - q^{14} + q^{15} - q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.