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Properties

Label 810.a
Number of curves $2$
Conductor $810$
CM no
Rank $0$
Graph

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

Elliptic curves in class 810.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
810.a1 810b2 \([1, -1, 0, -339, -4555]\) \(-8120601/12800\) \(-6802444800\) \([]\) \(648\) \(0.57799\)  
810.a2 810b1 \([1, -1, 0, 36, 120]\) \(62710839/125000\) \(-10125000\) \([3]\) \(216\) \(0.028683\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 810.a have rank \(0\).

Complex multiplication

The elliptic curves in class 810.a do not have complex multiplication.

Modular form 810.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - 4 q^{7} - q^{8} - q^{10} + 3 q^{11} - 4 q^{13} + 4 q^{14} + q^{16} + 3 q^{17} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.