Properties

Label 377520.dy
Number of curves $4$
Conductor $377520$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 377520.dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.dy1 377520dy3 \([0, 1, 0, -3104963616, 66592625380884]\) \(912446049969377120252018/17177299425\) \(62321937913144166400\) \([2]\) \(165150720\) \(3.7863\)  
377520.dy2 377520dy4 \([0, 1, 0, -211369616, 843820298484]\) \(287849398425814280018/81784533026485575\) \(296727120103288446428313600\) \([2]\) \(165150720\) \(3.7863\)  
377520.dy3 377520dy2 \([0, 1, 0, -194066616, 1040389299684]\) \(445574312599094932036/61129333175625\) \(110893406832582042240000\) \([2, 2]\) \(82575360\) \(3.4397\)  
377520.dy4 377520dy1 \([0, 1, 0, -11054116, 19252754684]\) \(-329381898333928144/162600887109375\) \(-73742691883103100000000\) \([2]\) \(41287680\) \(3.0931\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 377520.dy have rank \(1\).

Complex multiplication

The elliptic curves in class 377520.dy do not have complex multiplication.

Modular form 377520.2.a.dy

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.