# Properties

 Label 361b Number of curves $3$ Conductor $361$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 361b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361.b3 361b1 $$[0, -1, 1, 241, -17]$$ $$32768/19$$ $$-893871739$$ $$[]$$ $$120$$ $$0.40705$$ $$\Gamma_0(N)$$-optimal
361.b2 361b2 $$[0, -1, 1, -3369, 81208]$$ $$-89915392/6859$$ $$-322687697779$$ $$[]$$ $$360$$ $$0.95635$$
361.b1 361b3 $$[0, -1, 1, -277729, 56427893]$$ $$-50357871050752/19$$ $$-893871739$$ $$[]$$ $$1080$$ $$1.5057$$

## Rank

sage: E.rank()

The elliptic curves in class 361b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 361b do not have complex multiplication.

## Modular form361.2.a.b

sage: E.q_eigenform(10)

$$q + 2q^{3} - 2q^{4} + 3q^{5} - q^{7} + q^{9} + 3q^{11} - 4q^{12} + 4q^{13} + 6q^{15} + 4q^{16} - 3q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 