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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 44400.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.bw1 | 44400cn4 | \([0, 1, 0, -4195008, 1474823988]\) | \(127568139540190201/59114336463360\) | \(3783317533655040000000\) | \([2]\) | \(3483648\) | \(2.8350\) | |
44400.bw2 | 44400cn2 | \([0, 1, 0, -2125008, -1192956012]\) | \(16581570075765001/998001000\) | \(63872064000000000\) | \([2]\) | \(1161216\) | \(2.2857\) | |
44400.bw3 | 44400cn1 | \([0, 1, 0, -125008, -20956012]\) | \(-3375675045001/999000000\) | \(-63936000000000000\) | \([2]\) | \(580608\) | \(1.9391\) | \(\Gamma_0(N)\)-optimal |
44400.bw4 | 44400cn3 | \([0, 1, 0, 924992, 174343988]\) | \(1367594037332999/995878502400\) | \(-63736224153600000000\) | \([2]\) | \(1741824\) | \(2.4884\) |
Rank
sage: E.rank()
The elliptic curves in class 44400.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 44400.bw do not have complex multiplication.Modular form 44400.2.a.bw
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.