Properties

Label 301530.cj
Number of curves $4$
Conductor $301530$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 301530.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.cj1 301530cj3 \([1, 1, 1, -328520, 72233207]\) \(26487576322129/44531250\) \(6592223182031250\) \([2]\) \(3153920\) \(1.9307\)  
301530.cj2 301530cj2 \([1, 1, 1, -26990, 348455]\) \(14688124849/8122500\) \(1202421508402500\) \([2, 2]\) \(1576960\) \(1.5841\)  
301530.cj3 301530cj1 \([1, 1, 1, -16410, -811113]\) \(3301293169/22800\) \(3375218269200\) \([2]\) \(788480\) \(1.2375\) \(\Gamma_0(N)\)-optimal
301530.cj4 301530cj4 \([1, 1, 1, 105260, 2887655]\) \(871257511151/527800050\) \(-78133349615994450\) \([2]\) \(3153920\) \(1.9307\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301530.cj have rank \(1\).

Complex multiplication

The elliptic curves in class 301530.cj do not have complex multiplication.

Modular form 301530.2.a.cj

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 2q^{13} - q^{15} + q^{16} - 2q^{17} + q^{18} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.