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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 37830.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37830.w1 | 37830x1 | \([1, 0, 0, -172971, 27674865]\) | \(-572326371539096052529/5361176808000\) | \(-5361176808000\) | \([3]\) | \(186624\) | \(1.6056\) | \(\Gamma_0(N)\)-optimal |
37830.w2 | 37830x2 | \([1, 0, 0, -87111, 55084941]\) | \(-73104316609809474289/1268879289539062500\) | \(-1268879289539062500\) | \([]\) | \(559872\) | \(2.1549\) |
Rank
sage: E.rank()
The elliptic curves in class 37830.w have rank \(1\).
Complex multiplication
The elliptic curves in class 37830.w do not have complex multiplication.Modular form 37830.2.a.w
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.