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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 83790.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.t1 | 83790bl1 | \([1, -1, 0, -928755, 316916725]\) | \(1033027067767969/92665036800\) | \(7947520758658252800\) | \([2]\) | \(1720320\) | \(2.3663\) | \(\Gamma_0(N)\)-optimal |
83790.t2 | 83790bl2 | \([1, -1, 0, 1046925, 1482963061]\) | \(1479634409024351/11937345840000\) | \(-1023819847732286640000\) | \([2]\) | \(3440640\) | \(2.7129\) |
Rank
sage: E.rank()
The elliptic curves in class 83790.t have rank \(0\).
Complex multiplication
The elliptic curves in class 83790.t do not have complex multiplication.Modular form 83790.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.