Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 304.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304.c1 304b3 \([0, -1, 0, -1368, 157168]\) \(-69173457625/2550136832\) \(-10445360463872\) \([]\) \(432\) \(1.1783\)  
304.c2 304b1 \([0, -1, 0, -248, -1424]\) \(-413493625/152\) \(-622592\) \([]\) \(48\) \(0.079705\) \(\Gamma_0(N)\)-optimal
304.c3 304b2 \([0, -1, 0, 152, -5776]\) \(94196375/3511808\) \(-14384365568\) \([]\) \(144\) \(0.62901\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 304.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.