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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 55825.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55825.t1 | 55825l4 | \([1, -1, 0, -1333892, 593233641]\) | \(16798320881842096017/2132227789307\) | \(33316059207921875\) | \([2]\) | \(688128\) | \(2.1922\) | |
| 55825.t2 | 55825l3 | \([1, -1, 0, -529142, -141967109]\) | \(1048626554636928177/48569076788309\) | \(758891824817328125\) | \([2]\) | \(688128\) | \(2.1922\) | |
| 55825.t3 | 55825l2 | \([1, -1, 0, -90517, 7604016]\) | \(5249244962308257/1448621666569\) | \(22634713540140625\) | \([2, 2]\) | \(344064\) | \(1.8457\) | |
| 55825.t4 | 55825l1 | \([1, -1, 0, 14608, 770891]\) | \(22062729659823/29354283343\) | \(-458660677234375\) | \([2]\) | \(172032\) | \(1.4991\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55825.t have rank \(1\).
Complex multiplication
The elliptic curves in class 55825.t do not have complex multiplication.Modular form 55825.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
