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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 127050.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.bm1 | 127050v2 | \([1, 1, 0, -1060325, 444202125]\) | \(-7620530425/526848\) | \(-9114681345000000000\) | \([]\) | \(3499200\) | \(2.3890\) | |
127050.bm2 | 127050v1 | \([1, 1, 0, 74050, 661500]\) | \(2595575/1512\) | \(-26158205390625000\) | \([]\) | \(1166400\) | \(1.8397\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127050.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 127050.bm do not have complex multiplication.Modular form 127050.2.a.bm
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.