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Properties

Label 75810.o
Number of curves $2$
Conductor $75810$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 75810.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75810.o1 75810i1 \([1, 1, 0, -2379358, 1410794848]\) \(4616586342451/3307500\) \(1067289560404042500\) \([2]\) \(2626560\) \(2.3946\) \(\Gamma_0(N)\)-optimal
75810.o2 75810i2 \([1, 1, 0, -1899228, 1997417682]\) \(-2347864201171/3986718750\) \(-1286465095129872656250\) \([2]\) \(5253120\) \(2.7412\)  

Rank

sage: E.rank()
 

The elliptic curves in class 75810.o have rank \(0\).

Complex multiplication

The elliptic curves in class 75810.o do not have complex multiplication.

Modular form 75810.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} - q^{14} + q^{15} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.