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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 46200.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.bx1 | 46200cl4 | \([0, 1, 0, -407367408, -2803021257312]\) | \(233632133015204766393938/29145526885986328125\) | \(932656860351562500000000000\) | \([2]\) | \(23592960\) | \(3.9047\) | |
| 46200.bx2 | 46200cl2 | \([0, 1, 0, -101754408, 349682450688]\) | \(7282213870869695463556/912102595400390625\) | \(14593641526406250000000000\) | \([2, 2]\) | \(11796480\) | \(3.5581\) | |
| 46200.bx3 | 46200cl1 | \([0, 1, 0, -98473908, 376083914688]\) | \(26401417552259125806544/507547744790625\) | \(2030190979162500000000\) | \([4]\) | \(5898240\) | \(3.2115\) | \(\Gamma_0(N)\)-optimal |
| 46200.bx4 | 46200cl3 | \([0, 1, 0, 151370592, 1812744950688]\) | \(11986661998777424518222/51295853620928503125\) | \(-1641467315869712100000000000\) | \([2]\) | \(23592960\) | \(3.9047\) |
Rank
sage: E.rank()
The elliptic curves in class 46200.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 46200.bx do not have complex multiplication.Modular form 46200.2.a.bx
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.
