# Properties

 Label 1380.b Number of curves $2$ Conductor $1380$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1380.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1380.b1 1380a1 $$[0, -1, 0, -21, -30]$$ $$67108864/1725$$ $$27600$$ $$$$ $$120$$ $$-0.36567$$ $$\Gamma_0(N)$$-optimal
1380.b2 1380a2 $$[0, -1, 0, 4, -120]$$ $$21296/23805$$ $$-6094080$$ $$$$ $$240$$ $$-0.019099$$

## Rank

sage: E.rank()

The elliptic curves in class 1380.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1380.b do not have complex multiplication.

## Modular form1380.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 6 q^{13} + q^{15} + 2 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 