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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 64350.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64350.t1 | 64350bm4 | \([1, -1, 0, -511103817, 4447585211341]\) | \(1296294060988412126189641/647824320\) | \(7379123895000000\) | \([2]\) | \(7962624\) | \(3.2809\) | |
| 64350.t2 | 64350bm3 | \([1, -1, 0, -31943817, 69500291341]\) | \(-316472948332146183241/7074906009600\) | \(-80587601265600000000\) | \([2]\) | \(3981312\) | \(2.9343\) | |
| 64350.t3 | 64350bm2 | \([1, -1, 0, -6321942, 6077938216]\) | \(2453170411237305241/19353090685500\) | \(220443798589523437500\) | \([2]\) | \(2654208\) | \(2.7316\) | |
| 64350.t4 | 64350bm1 | \([1, -1, 0, -134442, 218375716]\) | \(-23592983745241/1794399750000\) | \(-20439334652343750000\) | \([2]\) | \(1327104\) | \(2.3850\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64350.t have rank \(1\).
Complex multiplication
The elliptic curves in class 64350.t do not have complex multiplication.Modular form 64350.2.a.t
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.
