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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 76050.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.w1 | 76050cr2 | \([1, -1, 0, -190917, 32156541]\) | \(-349938025/8\) | \(-17593718805000\) | \([]\) | \(388800\) | \(1.6550\) | |
76050.w2 | 76050cr3 | \([1, -1, 0, -114867, -18036459]\) | \(-121945/32\) | \(-43984297012500000\) | \([]\) | \(648000\) | \(1.9104\) | |
76050.w3 | 76050cr1 | \([1, -1, 0, -792, 101466]\) | \(-25/2\) | \(-4398429701250\) | \([]\) | \(129600\) | \(1.1057\) | \(\Gamma_0(N)\)-optimal |
76050.w4 | 76050cr4 | \([1, -1, 0, 835758, 133112916]\) | \(46969655/32768\) | \(-45039920140800000000\) | \([]\) | \(1944000\) | \(2.4597\) |
Rank
sage: E.rank()
The elliptic curves in class 76050.w have rank \(1\).
Complex multiplication
The elliptic curves in class 76050.w do not have complex multiplication.Modular form 76050.2.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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.