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Properties

Label 321346.c
Number of curves $2$
Conductor $321346$
CM no
Rank $1$
Graph

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

Elliptic curves in class 321346.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
321346.c1 321346c2 \([1, 1, 1, -3358, 72697]\) \(4187683692006625/51631625858\) \(51631625858\) \([2]\) \(512384\) \(0.86574\)  
321346.c2 321346c1 \([1, 1, 1, -3348, 73169]\) \(4150382922402625/642692\) \(642692\) \([2]\) \(256192\) \(0.51917\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 321346.c have rank \(1\).

Complex multiplication

The elliptic curves in class 321346.c do not have complex multiplication.

Modular form 321346.2.a.c

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