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Properties

Label 12882.f
Number of curves $2$
Conductor $12882$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 12882.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12882.f1 12882i2 \([1, 0, 1, -2529056, -832121746]\) \(1788952473315990499029625/736296634487918297088\) \(736296634487918297088\) \([]\) \(609120\) \(2.7015\)  
12882.f2 12882i1 \([1, 0, 1, -1171361, 487820180]\) \(177744208950637895247625/17681950027579392\) \(17681950027579392\) \([3]\) \(203040\) \(2.1521\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12882.f have rank \(0\).

Complex multiplication

The elliptic curves in class 12882.f do not have complex multiplication.

Modular form 12882.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} + 2 q^{13} + q^{14} + q^{16} - 3 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.