Properties

Label 303600.e
Number of curves $4$
Conductor $303600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 303600.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303600.e1 303600e4 \([0, -1, 0, -489533008, -932231271488]\) \(202716771344720336812681/111444770370514561200\) \(7132465303712931916800000000\) \([2]\) \(259522560\) \(4.0352\)  
303600.e2 303600e2 \([0, -1, 0, -295133008, 1939445528512]\) \(44421896119170051148681/319911052206240000\) \(20474307341199360000000000\) \([2, 2]\) \(129761280\) \(3.6886\)  
303600.e3 303600e1 \([0, -1, 0, -294621008, 1946550040512]\) \(44191106172662624762761/2316725452800\) \(148270428979200000000\) \([2]\) \(64880640\) \(3.3420\) \(\Gamma_0(N)\)-optimal
303600.e4 303600e3 \([0, -1, 0, -108925008, 4356425368512]\) \(-2233194469464162213001/126809990183868750000\) \(-8115839371767600000000000000\) \([2]\) \(259522560\) \(4.0352\)  

Rank

sage: E.rank()
 

The elliptic curves in class 303600.e have rank \(1\).

Complex multiplication

The elliptic curves in class 303600.e do not have complex multiplication.

Modular form 303600.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - q^{11} - 6 q^{13} - 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.