Properties

Label 37440dc
Number of curves $2$
Conductor $37440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 37440dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.t2 37440dc1 \([0, 0, 0, -1548, 26128]\) \(-57960603/8125\) \(-57507840000\) \([2]\) \(32768\) \(0.79593\) \(\Gamma_0(N)\)-optimal
37440.t1 37440dc2 \([0, 0, 0, -25548, 1571728]\) \(260549802603/4225\) \(29904076800\) \([2]\) \(65536\) \(1.1425\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37440dc have rank \(1\).

Complex multiplication

The elliptic curves in class 37440dc do not have complex multiplication.

Modular form 37440.2.a.dc

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} + 4 q^{11} + q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.