Properties

Label 1380.d
Number of curves $4$
Conductor $1380$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1380.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1380.d1 1380d3 \([0, 1, 0, -12165, -520512]\) \(12444451776495616/912525\) \(14600400\) \([2]\) \(1512\) \(0.82545\)  
1380.d2 1380d4 \([0, 1, 0, -12140, -522732]\) \(-772993034343376/6661615005\) \(-1705373441280\) \([2]\) \(3024\) \(1.1720\)  
1380.d3 1380d1 \([0, 1, 0, -165, -612]\) \(31238127616/9703125\) \(155250000\) \([6]\) \(504\) \(0.27614\) \(\Gamma_0(N)\)-optimal
1380.d4 1380d2 \([0, 1, 0, 460, -3612]\) \(41957807024/48205125\) \(-12340512000\) \([6]\) \(1008\) \(0.62271\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1380.d have rank \(0\).

Complex multiplication

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

Modular form 1380.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 4 q^{7} + q^{9} + 2 q^{13} + q^{15} + 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.