Properties

Label 2304.i
Number of curves $2$
Conductor $2304$
CM \(\Q(\sqrt{-2}) \)
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2304.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
2304.i1 2304c2 \([0, 0, 0, -120, 448]\) \(8000\) \(23887872\) \([2]\) \(384\) \(0.14533\)   \(-8\)
2304.i2 2304c1 \([0, 0, 0, -30, -56]\) \(8000\) \(373248\) \([2]\) \(192\) \(-0.20124\) \(\Gamma_0(N)\)-optimal \(-8\)

Rank

sage: E.rank()
 

The elliptic curves in class 2304.i have rank \(0\).

Complex multiplication

Each elliptic curve in class 2304.i has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 2304.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.