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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 348480.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.t1 | 348480t4 | \([0, 0, 0, -127746218028, -17572818472848848]\) | \(680995599504466943307169/52207031250000000\) | \(17674720671421440000000000000000\) | \([2]\) | \(1651507200\) | \(5.0440\) | |
| 348480.t2 | 348480t2 | \([0, 0, 0, -8515876908, -235916107681232]\) | \(201738262891771037089/45727545600000000\) | \(15481087051271211948441600000000\) | \([2, 2]\) | \(825753600\) | \(4.6975\) | |
| 348480.t3 | 348480t1 | \([0, 0, 0, -2806380588, 54064642814512]\) | \(7220044159551112609/448454983680000\) | \(151824694499380493266452480000\) | \([2]\) | \(412876800\) | \(4.3509\) | \(\Gamma_0(N)\)-optimal |
| 348480.t4 | 348480t3 | \([0, 0, 0, 19362523092, -1457781774241232]\) | \(2371297246710590562911/4084000833203280000\) | \(-1382640847801902113944586158080000\) | \([2]\) | \(1651507200\) | \(5.0440\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.t have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.t do not have complex multiplication.Modular form 348480.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
