Properties

Label 1380.c
Number of curves $2$
Conductor $1380$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1380.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1380.c1 1380c2 \([0, 1, 0, -1381, -20425]\) \(-1138621087744/13687875\) \(-3504096000\) \([]\) \(864\) \(0.64321\)  
1380.c2 1380c1 \([0, 1, 0, 59, -121]\) \(87228416/83835\) \(-21461760\) \([3]\) \(288\) \(0.093906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1380.c have rank \(1\).

Complex multiplication

The elliptic curves in class 1380.c do not have complex multiplication.

Modular form 1380.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - 4 q^{13} - q^{15} - 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.