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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 75150.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75150.bs1 | 75150bm1 | \([1, -1, 1, -140, -1353]\) | \(-16539745/36072\) | \(-657412200\) | \([]\) | \(47232\) | \(0.38077\) | \(\Gamma_0(N)\)-optimal |
75150.bs2 | 75150bm2 | \([1, -1, 1, 1210, 29967]\) | \(10758425855/27944778\) | \(-509293579050\) | \([]\) | \(141696\) | \(0.93008\) |
Rank
sage: E.rank()
The elliptic curves in class 75150.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 75150.bs do not have complex multiplication.Modular form 75150.2.a.bs
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.