# Properties

 Label 26520.x Number of curves $4$ Conductor $26520$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 26520.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.x1 26520f4 $$[0, 1, 0, -62496, -6034320]$$ $$26362547147244676/244298925$$ $$250162099200$$ $$[2]$$ $$73728$$ $$1.3508$$
26520.x2 26520f2 $$[0, 1, 0, -3996, -90720]$$ $$27572037674704/2472575625$$ $$632979360000$$ $$[2, 2]$$ $$36864$$ $$1.0042$$
26520.x3 26520f1 $$[0, 1, 0, -871, 8030]$$ $$4572531595264/776953125$$ $$12431250000$$ $$[2]$$ $$18432$$ $$0.65763$$ $$\Gamma_0(N)$$-optimal
26520.x4 26520f3 $$[0, 1, 0, 4504, -417120]$$ $$9865576607324/79640206425$$ $$-81551571379200$$ $$[4]$$ $$73728$$ $$1.3508$$

## Rank

sage: E.rank()

The elliptic curves in class 26520.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 26520.x do not have complex multiplication.

## Modular form 26520.2.a.x

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} - q^{15} + q^{17} - 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.