Label 2304p
Number of curves $2$
Conductor $2304$
CM \(\Q(\sqrt{-1}) \)
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
sage: E.isogeny_class()

Elliptic curves in class 2304p

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality CM discriminant
2304.a2 2304p1 [0, 0, 0, 18, 0] [2] 256 \(\Gamma_0(N)\)-optimal -4
2304.a1 2304p2 [0, 0, 0, -72, 0] [2] 512   -4


sage: E.rank()

The elliptic curves in class 2304p have rank \(1\).

Complex multiplication

Each elliptic curve in class 2304p has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 2304.2.a.p

sage: E.q_eigenform(10)
\(q - 4q^{5} + 4q^{13} + 2q^{17} + O(q^{20})\)  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 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.