# Properties

 Label 1815.b Number of curves $2$ Conductor $1815$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 1815.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1815.b1 1815e2 $$[0, 1, 1, -724951, -237822920]$$ $$-196566176333824/421875$$ $$-90432652921875$$ $$[]$$ $$14256$$ $$1.9255$$
1815.b2 1815e1 $$[0, 1, 1, -6211, -530909]$$ $$-123633664/492075$$ $$-105480646368075$$ $$$$ $$4752$$ $$1.3762$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1815.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1815.b do not have complex multiplication.

## Modular form1815.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} - q^{5} - q^{7} + q^{9} - 2q^{12} + 2q^{13} - q^{15} + 4q^{16} + 6q^{17} - 7q^{19} + O(q^{20})$$ ## 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. 