Properties

Label 302016.fl
Number of curves $4$
Conductor $302016$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fl1")
 
E.isogeny_class()
 

Elliptic curves in class 302016.fl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
302016.fl1 302016fl4 \([0, 1, 0, -504719233, -4364098531201]\) \(30618029936661765625/3678951124992\) \(1708519937524879199305728\) \([2]\) \(79626240\) \(3.6745\)  
302016.fl2 302016fl3 \([0, 1, 0, -28927873, -79977967489]\) \(-5764706497797625/2612665516032\) \(-1213332543044889071321088\) \([2]\) \(39813120\) \(3.3279\)  
302016.fl3 302016fl2 \([0, 1, 0, -13943233, 11412933695]\) \(645532578015625/252306960048\) \(117172383370338612805632\) \([2]\) \(26542080\) \(3.1252\)  
302016.fl4 302016fl1 \([0, 1, 0, 2783807, 1286383679]\) \(5137417856375/4510142208\) \(-2094528473372213379072\) \([2]\) \(13271040\) \(2.7786\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 302016.fl have rank \(1\).

Complex multiplication

The elliptic curves in class 302016.fl do not have complex multiplication.

Modular form 302016.2.a.fl

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.