Properties

Label 1323.l
Number of curves $3$
Conductor $1323$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1323.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1323.l1 1323c3 \([0, 0, 1, -187866, 31341539]\) \(35184082944/7\) \(145888171821\) \([]\) \(5184\) \(1.5316\)  
1323.l2 1323c2 \([0, 0, 1, -2646, 30098]\) \(884736/343\) \(794280046581\) \([]\) \(1728\) \(0.98228\)  
1323.l3 1323c1 \([0, 0, 1, -1176, -15521]\) \(56623104/7\) \(22235661\) \([]\) \(576\) \(0.43298\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1323.l have rank \(0\).

Complex multiplication

The elliptic curves in class 1323.l do not have complex multiplication.

Modular form 1323.2.a.l

sage: E.q_eigenform(10)
 
\(q - 2q^{4} + 3q^{5} - 6q^{11} + 4q^{13} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.