Properties

 Label 19600h Number of curves $4$ Conductor $19600$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 19600h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.cj4 19600h1 [0, 0, 0, 1225, 85750] [2] 24576 $$\Gamma_0(N)$$-optimal
19600.cj3 19600h2 [0, 0, 0, -23275, 1286250] [2, 2] 49152
19600.cj2 19600h3 [0, 0, 0, -72275, -5916750] [2] 98304
19600.cj1 19600h4 [0, 0, 0, -366275, 85321250] [2] 98304

Rank

sage: E.rank()

The elliptic curves in class 19600h have rank $$0$$.

Complex multiplication

The elliptic curves in class 19600h do not have complex multiplication.

Modular form 19600.2.a.h

sage: E.q_eigenform(10)

$$q - 3q^{9} + 4q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.