Properties

 Label 26520.z Number of curves $4$ Conductor $26520$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

Elliptic curves in class 26520.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.z1 26520bb4 $$[0, 1, 0, -2040056, -1122211200]$$ $$916959671620739147236/2731145625$$ $$2796693120000$$ $$$$ $$393216$$ $$2.0417$$
26520.z2 26520bb2 $$[0, 1, 0, -127556, -17551200]$$ $$896581610757188944/1545359765625$$ $$395612100000000$$ $$[2, 2]$$ $$196608$$ $$1.6951$$
26520.z3 26520bb3 $$[0, 1, 0, -87776, -28657776]$$ $$-73039208963041156/303497314453125$$ $$-310781250000000000$$ $$$$ $$393216$$ $$2.0417$$
26520.z4 26520bb1 $$[0, 1, 0, -10511, -88086]$$ $$8027441608013824/4452347908125$$ $$71237566530000$$ $$$$ $$98304$$ $$1.3485$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 26520.2.a.z

sage: E.q_eigenform(10)

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