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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 104742.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.bv1 | 104742bl3 | \([1, -1, 1, -383360, -90914461]\) | \(57736239625/255552\) | \(27578702411675712\) | \([2]\) | \(1140480\) | \(2.0070\) | |
104742.bv2 | 104742bl4 | \([1, -1, 1, -192920, -181411549]\) | \(-7357983625/127552392\) | \(-13765219841227639752\) | \([2]\) | \(2280960\) | \(2.3535\) | |
104742.bv3 | 104742bl1 | \([1, -1, 1, -26285, 1553681]\) | \(18609625/1188\) | \(128206777740228\) | \([2]\) | \(380160\) | \(1.4577\) | \(\Gamma_0(N)\)-optimal |
104742.bv4 | 104742bl2 | \([1, -1, 1, 21325, 6524165]\) | \(9938375/176418\) | \(-19038706494423858\) | \([2]\) | \(760320\) | \(1.8042\) |
Rank
sage: E.rank()
The elliptic curves in class 104742.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 104742.bv do not have complex multiplication.Modular form 104742.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.