Properties

Label 38640.m
Number of curves $2$
Conductor $38640$
CM no
Rank $1$
Graph

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

Elliptic curves in class 38640.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.m1 38640bk1 \([0, -1, 0, -376, -1424]\) \(1439069689/579600\) \(2374041600\) \([2]\) \(18432\) \(0.49695\) \(\Gamma_0(N)\)-optimal
38640.m2 38640bk2 \([0, -1, 0, 1224, -11664]\) \(49471280711/41992020\) \(-171999313920\) \([2]\) \(36864\) \(0.84352\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38640.m have rank \(1\).

Complex multiplication

The elliptic curves in class 38640.m do not have complex multiplication.

Modular form 38640.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 2q^{11} + 4q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.