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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 76050ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.dt2 | 76050ev1 | \([1, -1, 1, -540415895, 5297616881327]\) | \(-198417696411528597145/22989483914821632\) | \(-2022352577347211825695948800\) | \([]\) | \(45158400\) | \(3.9758\) | \(\Gamma_0(N)\)-optimal |
76050.dt1 | 76050ev2 | \([1, -1, 1, -346645426055, 78555537376538447]\) | \(-134057911417971280740025/1872\) | \(-64327034380781250000\) | \([]\) | \(225792000\) | \(4.7805\) |
Rank
sage: E.rank()
The elliptic curves in class 76050ev have rank \(1\).
Complex multiplication
The elliptic curves in class 76050ev do not have complex multiplication.Modular form 76050.2.a.ev
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.