# Properties

 Label 370.b Number of curves $4$ Conductor $370$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 370.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370.b1 370a3 $$[1, -1, 0, -395, -2925]$$ $$6825481747209/46250$$ $$46250$$ $$$$ $$64$$ $$0.076511$$
370.b2 370a2 $$[1, -1, 0, -25, -39]$$ $$1767172329/136900$$ $$136900$$ $$[2, 2]$$ $$32$$ $$-0.27006$$
370.b3 370a1 $$[1, -1, 0, -5, 5]$$ $$15438249/2960$$ $$2960$$ $$$$ $$16$$ $$-0.61664$$ $$\Gamma_0(N)$$-optimal
370.b4 370a4 $$[1, -1, 0, 25, -209]$$ $$1689410871/18741610$$ $$-18741610$$ $$$$ $$64$$ $$0.076511$$

## Rank

sage: E.rank()

The elliptic curves in class 370.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 370.b do not have complex multiplication.

## Modular form370.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} - 3q^{9} + q^{10} - 4q^{11} + 2q^{13} + q^{16} - 2q^{17} + 3q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 