# Properties

 Label 18515.o Number of curves $3$ Conductor $18515$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 18515.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.o1 18515i3 $$[0, 1, 1, -69475, 7350156]$$ $$-250523582464/13671875$$ $$-2023928169921875$$ $$[]$$ $$71280$$ $$1.6952$$
18515.o2 18515i1 $$[0, 1, 1, -705, -8234]$$ $$-262144/35$$ $$-5181256115$$ $$[]$$ $$7920$$ $$0.59660$$ $$\Gamma_0(N)$$-optimal
18515.o3 18515i2 $$[0, 1, 1, 4585, 21919]$$ $$71991296/42875$$ $$-6347038740875$$ $$[]$$ $$23760$$ $$1.1459$$

## Rank

sage: E.rank()

The elliptic curves in class 18515.o have rank $$1$$.

## Complex multiplication

The elliptic curves in class 18515.o do not have complex multiplication.

## Modular form 18515.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + q^{5} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} + 5q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 