# Properties

 Label 38115.q Number of curves $3$ Conductor $38115$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 38115.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38115.q1 38115y3 $$[0, 0, 1, -143022, -21778155]$$ $$-250523582464/13671875$$ $$-17656788638671875$$ $$[]$$ $$243000$$ $$1.8757$$
38115.q2 38115y1 $$[0, 0, 1, -1452, 23625]$$ $$-262144/35$$ $$-45201378915$$ $$[]$$ $$27000$$ $$0.77710$$ $$\Gamma_0(N)$$-optimal
38115.q3 38115y2 $$[0, 0, 1, 9438, -60228]$$ $$71991296/42875$$ $$-55371689170875$$ $$[]$$ $$81000$$ $$1.3264$$

## Rank

sage: E.rank()

The elliptic curves in class 38115.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 38115.q do not have complex multiplication.

## Modular form 38115.2.a.q

sage: E.q_eigenform(10)

$$q - 2q^{4} + q^{5} - q^{7} - 5q^{13} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 