# Properties

 Label 390775.bm Number of curves $4$ Conductor $390775$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 390775.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390775.bm1 390775bm4 $$[1, -1, 0, -65360717, -203348417434]$$ $$16798320881842096017/2132227789307$$ $$3919601049752800671875$$ $$[2]$$ $$33030144$$ $$3.1652$$
390775.bm2 390775bm3 $$[1, -1, 0, -25927967, 48746574316]$$ $$1048626554636928177/48569076788309$$ $$89282864297933836578125$$ $$[2]$$ $$33030144$$ $$3.1652$$
390775.bm3 390775bm2 $$[1, -1, 0, -4435342, -2599306809]$$ $$5249244962308257/1448621666569$$ $$2662951413284004390625$$ $$[2, 2]$$ $$16515072$$ $$2.8186$$
390775.bm4 390775bm1 $$[1, -1, 0, 715783, -265847184]$$ $$22062729659823/29354283343$$ $$-53960970015946984375$$ $$[2]$$ $$8257536$$ $$2.4720$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 390775.bm have rank $$1$$.

## Complex multiplication

The elliptic curves in class 390775.bm do not have complex multiplication.

## Modular form 390775.2.a.bm

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 3q^{8} - 3q^{9} - q^{11} + 6q^{13} - q^{16} - 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.