Properties

Label 324.b
Number of curves $2$
Conductor $324$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 324.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324.b1 324d1 \([0, 0, 0, -39, 94]\) \(-316368\) \(-20736\) \([3]\) \(36\) \(-0.30456\) \(\Gamma_0(N)\)-optimal
324.b2 324d2 \([0, 0, 0, 81, 486]\) \(432\) \(-136048896\) \([]\) \(108\) \(0.24475\)  

Rank

sage: E.rank()
 

The elliptic curves in class 324.b have rank \(0\).

Complex multiplication

The elliptic curves in class 324.b do not have complex multiplication.

Modular form 324.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.