# Properties

 Label 114240.fb Number of curves 4 Conductor 114240 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("114240.fb1")

sage: E.isogeny_class()

## Elliptic curves in class 114240.fb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
114240.fb1 114240cd4 [0, -1, 0, -107905, 13678465]  524288
114240.fb2 114240cd3 [0, -1, 0, -34305, -2262015]  524288
114240.fb3 114240cd2 [0, -1, 0, -7105, 191425] [2, 2] 262144
114240.fb4 114240cd1 [0, -1, 0, 895, 17025]  131072 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 114240.fb have rank $$1$$.

## Modular form 114240.2.a.fb

sage: E.q_eigenform(10)

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

## 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. 