Properties

Label 33810da
Number of curves $2$
Conductor $33810$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33810da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.cs1 33810da1 \([1, 0, 0, -12006, -484380]\) \(1626794704081/83462400\) \(9819267897600\) \([2]\) \(147456\) \(1.2508\) \(\Gamma_0(N)\)-optimal
33810.cs2 33810da2 \([1, 0, 0, 7594, -1907340]\) \(411664745519/13605414480\) \(-1600663408157520\) \([2]\) \(294912\) \(1.5974\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33810da have rank \(1\).

Complex multiplication

The elliptic curves in class 33810da do not have complex multiplication.

Modular form 33810.2.a.da

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 6q^{11} + q^{12} - q^{15} + q^{16} - 6q^{17} + q^{18} + 8q^{19} + O(q^{20})\)  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 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.