# Properties

 Label 26520.v Number of curves $4$ Conductor $26520$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 26520.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.v1 26520c4 $$[0, 1, 0, -32696, -2286480]$$ $$1887517194957938/21849165$$ $$44747089920$$ $$[2]$$ $$49152$$ $$1.1949$$
26520.v2 26520c2 $$[0, 1, 0, -2096, -34320]$$ $$994958062276/98903025$$ $$101276697600$$ $$[2, 2]$$ $$24576$$ $$0.84829$$
26520.v3 26520c1 $$[0, 1, 0, -476, 3264]$$ $$46689225424/7249905$$ $$1855975680$$ $$[2]$$ $$12288$$ $$0.50172$$ $$\Gamma_0(N)$$-optimal
26520.v4 26520c3 $$[0, 1, 0, 2584, -161616]$$ $$931329171502/6107473125$$ $$-12508104960000$$ $$[2]$$ $$49152$$ $$1.1949$$

## Rank

sage: E.rank()

The elliptic curves in class 26520.v have rank $$1$$.

## Complex multiplication

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

## Modular form 26520.2.a.v

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.