Properties

Label 225318.c
Number of curves $2$
Conductor $225318$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 225318.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
225318.c1 225318bh1 \([1, 1, 0, -5568, -103860]\) \(1771561/612\) \(6596879781348\) \([2]\) \(841984\) \(1.1615\) \(\Gamma_0(N)\)-optimal
225318.c2 225318bh2 \([1, 1, 0, 16522, -700290]\) \(46268279/46818\) \(-504661303273122\) \([2]\) \(1683968\) \(1.5081\)  

Rank

sage: E.rank()
 

The elliptic curves in class 225318.c have rank \(0\).

Complex multiplication

The elliptic curves in class 225318.c do not have complex multiplication.

Modular form 225318.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 4 q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} - 4 q^{10} - q^{12} + 6 q^{13} + 2 q^{14} - 4 q^{15} + q^{16} - q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.