Properties

Label 304.f
Number of curves $3$
Conductor $304$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 304.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304.f1 304e3 \([0, -1, 0, -12309, 529757]\) \(-50357871050752/19\) \(-77824\) \([]\) \(216\) \(0.72659\)  
304.f2 304e2 \([0, -1, 0, -149, 797]\) \(-89915392/6859\) \(-28094464\) \([]\) \(72\) \(0.17728\)  
304.f3 304e1 \([0, -1, 0, 11, -3]\) \(32768/19\) \(-77824\) \([]\) \(24\) \(-0.37203\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 304.f have rank \(0\).

Complex multiplication

The elliptic curves in class 304.f do not have complex multiplication.

Modular form 304.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + 3q^{5} + q^{7} + q^{9} - 3q^{11} - 4q^{13} + 6q^{15} - 3q^{17} - q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.