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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 101430u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.n1 | 101430u1 | \([1, -1, 0, -49518135, 134132672925]\) | \(156567200830221067489/16905000000\) | \(1449876275505000000\) | \([2]\) | \(6709248\) | \(2.9117\) | \(\Gamma_0(N)\)-optimal |
101430.n2 | 101430u2 | \([1, -1, 0, -49394655, 134834804901]\) | \(-155398856216042825569/1627294921875000\) | \(-139566773172216796875000\) | \([2]\) | \(13418496\) | \(3.2583\) |
Rank
sage: E.rank()
The elliptic curves in class 101430u have rank \(1\).
Complex multiplication
The elliptic curves in class 101430u do not have complex multiplication.Modular form 101430.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.