Properties

 Label 1152.i Number of curves $2$ Conductor $1152$ CM no Rank $1$ Graph

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1152.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1152.i1 1152r2 [0, 0, 0, -120, -416] [2] 256
1152.i2 1152r1 [0, 0, 0, 15, -38] [2] 128 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1152.i have rank $$1$$.

Complex multiplication

The elliptic curves in class 1152.i do not have complex multiplication.

Modular form1152.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{7} - 4q^{11} + 6q^{13} - 6q^{17} + O(q^{20})$$

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.