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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 5070.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5070.t1 | 5070t4 | \([1, 0, 0, -147465601, -689269402615]\) | \(73474353581350183614361/576510977802240\) | \(2782708376254652252160\) | \([2]\) | \(725760\) | \(3.2879\) | |
| 5070.t2 | 5070t3 | \([1, 0, 0, -9020801, -11249839095]\) | \(-16818951115904497561/1592332281446400\) | \(-7685883787076016537600\) | \([2]\) | \(362880\) | \(2.9413\) | |
| 5070.t3 | 5070t2 | \([1, 0, 0, -2704426, 64216580]\) | \(453198971846635561/261896250564000\) | \(1264123179288570276000\) | \([2]\) | \(241920\) | \(2.7386\) | |
| 5070.t4 | 5070t1 | \([1, 0, 0, 675574, 8108580]\) | \(7064514799444439/4094064000000\) | \(-19761264961776000000\) | \([2]\) | \(120960\) | \(2.3920\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5070.t have rank \(1\).
Complex multiplication
The elliptic curves in class 5070.t do not have complex multiplication.Modular form 5070.2.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.
