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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 51600.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.bv1 | 51600bw4 | \([0, -1, 0, -2201608, 1258089712]\) | \(18440127492397057/1032\) | \(66048000000\) | \([2]\) | \(737280\) | \(1.9909\) | |
51600.bv2 | 51600bw2 | \([0, -1, 0, -137608, 19689712]\) | \(4502751117697/1065024\) | \(68161536000000\) | \([2, 2]\) | \(368640\) | \(1.6444\) | |
51600.bv3 | 51600bw3 | \([0, -1, 0, -121608, 24425712]\) | \(-3107661785857/2215383048\) | \(-141784515072000000\) | \([2]\) | \(737280\) | \(1.9909\) | |
51600.bv4 | 51600bw1 | \([0, -1, 0, -9608, 233712]\) | \(1532808577/528384\) | \(33816576000000\) | \([2]\) | \(184320\) | \(1.2978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.bv do not have complex multiplication.Modular form 51600.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.