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Properties

Label 294.c
Number of curves $2$
Conductor $294$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 294.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
294.c1 294g2 \([1, 0, 1, -138, 592]\) \(838561807/26244\) \(9001692\) \([2]\) \(128\) \(0.10948\)  
294.c2 294g1 \([1, 0, 1, 2, 32]\) \(4913/1296\) \(-444528\) \([2]\) \(64\) \(-0.23709\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 294.c have rank \(1\).

Complex multiplication

The elliptic curves in class 294.c do not have complex multiplication.

Modular form 294.2.a.c

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