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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 37830.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37830.t1 | 37830t4 | \([1, 1, 1, -51086360, -140416795663]\) | \(14744789983875259660561223041/17756146316311322049000\) | \(17756146316311322049000\) | \([2]\) | \(6220800\) | \(3.1800\) | |
| 37830.t2 | 37830t3 | \([1, 1, 1, -36996360, 85905236337]\) | \(5600163455211446304650663041/51656524820538549951000\) | \(51656524820538549951000\) | \([2]\) | \(6220800\) | \(3.1800\) | |
| 37830.t3 | 37830t2 | \([1, 1, 1, -4041360, -937779663]\) | \(7299722233234506445943041/3845825372648961000000\) | \(3845825372648961000000\) | \([2, 2]\) | \(3110400\) | \(2.8334\) | |
| 37830.t4 | 37830t1 | \([1, 1, 1, 958640, -113779663]\) | \(97429466112745474056959/62014719000000000000\) | \(-62014719000000000000\) | \([4]\) | \(1555200\) | \(2.4868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37830.t have rank \(0\).
Complex multiplication
The elliptic curves in class 37830.t do not have complex multiplication.Modular form 37830.2.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.
