# Properties

 Label 7436.d Number of curves $2$ Conductor $7436$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7436.d1")

sage: E.isogeny_class()

## Elliptic curves in class 7436.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7436.d1 7436c2 [0, 1, 0, -13069, -582737] [] 12960
7436.d2 7436c1 [0, 1, 0, 451, -4081] [] 4320 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7436.d have rank $$1$$.

## Modular form7436.2.a.d

sage: E.q_eigenform(10)

$$q + q^{3} + 3q^{5} - 2q^{7} - 2q^{9} + q^{11} + 3q^{15} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.