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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 5775.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5775.t1 | 5775n5 | \([1, 0, 1, -112976, -14625277]\) | \(10206027697760497/5557167\) | \(86830734375\) | \([2]\) | \(20480\) | \(1.4275\) | |
| 5775.t2 | 5775n3 | \([1, 0, 1, -7101, -226277]\) | \(2533811507137/58110129\) | \(907970765625\) | \([2, 2]\) | \(10240\) | \(1.0809\) | |
| 5775.t3 | 5775n2 | \([1, 0, 1, -976, 6473]\) | \(6570725617/2614689\) | \(40854515625\) | \([2, 2]\) | \(5120\) | \(0.73436\) | |
| 5775.t4 | 5775n1 | \([1, 0, 1, -851, 9473]\) | \(4354703137/1617\) | \(25265625\) | \([2]\) | \(2560\) | \(0.38779\) | \(\Gamma_0(N)\)-optimal |
| 5775.t5 | 5775n6 | \([1, 0, 1, 774, -698777]\) | \(3288008303/13504609503\) | \(-211009523484375\) | \([2]\) | \(20480\) | \(1.4275\) | |
| 5775.t6 | 5775n4 | \([1, 0, 1, 3149, 47723]\) | \(221115865823/190238433\) | \(-2972475515625\) | \([2]\) | \(10240\) | \(1.0809\) |
Rank
sage: E.rank()
The elliptic curves in class 5775.t have rank \(0\).
Complex multiplication
The elliptic curves in class 5775.t do not have complex multiplication.Modular form 5775.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
