Properties

Label 304920.eu
Number of curves $4$
Conductor $304920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("eu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 304920.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304920.eu1 304920eu3 \([0, 0, 0, -32426427, 71060048246]\) \(1425631925916578/270703125\) \(715989842013600000000\) \([2]\) \(15728640\) \(3.0028\)  
304920.eu2 304920eu4 \([0, 0, 0, -14218347, -19982843386]\) \(120186986927618/4332064275\) \(11457991169662376908800\) \([2]\) \(15728640\) \(3.0028\)  
304920.eu3 304920eu2 \([0, 0, 0, -2239347, 863012414]\) \(939083699236/300155625\) \(396944768412339840000\) \([2, 2]\) \(7864320\) \(2.6562\)  
304920.eu4 304920eu1 \([0, 0, 0, 396033, 91900226]\) \(20777545136/23059575\) \(-7623859837760812800\) \([2]\) \(3932160\) \(2.3097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 304920.eu have rank \(0\).

Complex multiplication

The elliptic curves in class 304920.eu do not have complex multiplication.

Modular form 304920.2.a.eu

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