Properties

 Label 113715.bd Number of curves 4 Conductor 113715 CM no Rank 0 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("113715.bd1")

sage: E.isogeny_class()

Elliptic curves in class 113715.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
113715.bd1 113715t4 [1, -1, 0, -365580, -84981425] [2] 774144
113715.bd2 113715t2 [1, -1, 0, -24435, -1127984] [2, 2] 387072
113715.bd3 113715t1 [1, -1, 0, -8190, 272335] [2] 193536 $$\Gamma_0(N)$$-optimal
113715.bd4 113715t3 [1, -1, 0, 56790, -7089899] [2] 774144

Rank

sage: E.rank()

The elliptic curves in class 113715.bd have rank $$0$$.

Modular form 113715.2.a.bd

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - q^{5} + q^{7} - 3q^{8} - q^{10} + 6q^{13} + q^{14} - q^{16} - 2q^{17} + O(q^{20})$$

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.