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Properties

Label 12495.o
Number of curves $2$
Conductor $12495$
CM no
Rank $0$
Graph

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

Elliptic curves in class 12495.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12495.o1 12495o2 \([1, 0, 1, -29328, 1574563]\) \(23711636464489/4590075735\) \(540017820147015\) \([2]\) \(55296\) \(1.5439\)  
12495.o2 12495o1 \([1, 0, 1, 3747, 145723]\) \(49471280711/106269975\) \(-12502556288775\) \([2]\) \(27648\) \(1.1973\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12495.o have rank \(0\).

Complex multiplication

The elliptic curves in class 12495.o do not have complex multiplication.

Modular form 12495.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 4 q^{13} + q^{15} - q^{16} - q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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 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.