Properties

Label 305760.v
Number of curves $4$
Conductor $305760$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 305760.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
305760.v1 305760v4 \([0, -1, 0, -11148496, -14319428780]\) \(2543984126301795848/909361981125\) \(54776590191296064000\) \([2]\) \(14155776\) \(2.7567\)  
305760.v2 305760v2 \([0, -1, 0, -5758496, 5211309720]\) \(350584567631475848/8259273550125\) \(497507980236111936000\) \([2]\) \(14155776\) \(2.7567\)  
305760.v3 305760v1 \([0, -1, 0, -797246, -154778280]\) \(7442744143086784/2927948765625\) \(22046095636929000000\) \([2, 2]\) \(7077888\) \(2.4102\) \(\Gamma_0(N)\)-optimal
305760.v4 305760v3 \([0, -1, 0, 2556559, -1120003359]\) \(3834800837445824/3342041015625\) \(-1610497161000000000000\) \([2]\) \(14155776\) \(2.7567\)  

Rank

sage: E.rank()
 

The elliptic curves in class 305760.v have rank \(1\).

Complex multiplication

The elliptic curves in class 305760.v do not have complex multiplication.

Modular form 305760.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - q^{13} + q^{15} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.