Properties

Label 576g
Number of curves $2$
Conductor $576$
CM \(\Q(\sqrt{-1}) \)
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 576g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
576.a1 576g1 \([0, 0, 0, -27, 0]\) \(1728\) \(1259712\) \([2]\) \(96\) \(-0.14000\) \(\Gamma_0(N)\)-optimal \(-4\)
576.a2 576g2 \([0, 0, 0, 108, 0]\) \(1728\) \(-80621568\) \([2]\) \(192\) \(0.20657\)   \(-4\)

Rank

sage: E.rank()
 

The elliptic curves in class 576g have rank \(0\).

Complex multiplication

Each elliptic curve in class 576g has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 576.2.a.g

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + 6 q^{13} + 8 q^{17} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.