# Properties

 Label 76230cl Number of curves $4$ Conductor $76230$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cl1")

sage: E.isogeny_class()

## Elliptic curves in class 76230cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.ci3 76230cl1 [1, -1, 0, -3834, -56732] [2] 163840 $$\Gamma_0(N)$$-optimal
76230.ci2 76230cl2 [1, -1, 0, -25614, 1541920] [2, 2] 327680
76230.ci4 76230cl3 [1, -1, 0, 7056, 5181358] [2] 655360
76230.ci1 76230cl4 [1, -1, 0, -406764, 99954850] [2] 655360

## Rank

sage: E.rank()

The elliptic curves in class 76230cl have rank $$1$$.

## Complex multiplication

The elliptic curves in class 76230cl do not have complex multiplication.

## Modular form 76230.2.a.cl

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2q^{13} - q^{14} + q^{16} - 6q^{17} + O(q^{20})$$

## 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.