Properties

Label 147.c
Number of curves $2$
Conductor $147$
CM no
Rank $0$
Graph

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This isogeny class and its quadratic twist by $\Q(\sqrt{-3})$ are the ones of minimal conductor with a $13$-isogeny.

E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 147.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
147.c1 147b2 \([0, 1, 1, -44704, -3655907]\) \(-1713910976512/1594323\) \(-9190954824723\) \([]\) \(546\) \(1.4103\)  
147.c2 147b1 \([0, 1, 1, -114, 473]\) \(-28672/3\) \(-17294403\) \([]\) \(42\) \(0.12787\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 147.c have rank \(0\).

Complex multiplication

The elliptic curves in class 147.c do not have complex multiplication.

Modular form 147.2.a.c

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

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.