# Properties

 Label 19600ci Number of curves $3$ Conductor $19600$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ci1")

sage: E.isogeny_class()

## Elliptic curves in class 19600ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.br2 19600ci1 $$[0, -1, 0, -26133, 1812637]$$ $$-262144/35$$ $$-263533760000000$$ $$[]$$ $$55296$$ $$1.4997$$ $$\Gamma_0(N)$$-optimal
19600.br3 19600ci2 $$[0, -1, 0, 169867, -4655363]$$ $$71991296/42875$$ $$-322828856000000000$$ $$[]$$ $$165888$$ $$2.0490$$
19600.br1 19600ci3 $$[0, -1, 0, -2574133, -1662031363]$$ $$-250523582464/13671875$$ $$-102942875000000000000$$ $$[]$$ $$497664$$ $$2.5983$$

## Rank

sage: E.rank()

The elliptic curves in class 19600ci have rank $$1$$.

## Complex multiplication

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

## Modular form 19600.2.a.ci

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{9} + 3q^{11} + 5q^{13} + 3q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 