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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 348726.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348726.a1 | 348726a2 | \([1, 1, 0, -9754, 1688386]\) | \(-2181825073/25039686\) | \(-1178014087833366\) | \([]\) | \(2177280\) | \(1.5738\) | |
348726.a2 | 348726a1 | \([1, 1, 0, 1076, -59576]\) | \(2924207/34776\) | \(-1636067557656\) | \([]\) | \(725760\) | \(1.0245\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348726.a have rank \(1\).
Complex multiplication
The elliptic curves in class 348726.a do not have complex multiplication.Modular form 348726.2.a.a
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.