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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 10830.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.s1 | 10830t1 | \([1, 1, 1, -36, -111]\) | \(-14317849/2700\) | \(-974700\) | \([]\) | \(2592\) | \(-0.12672\) | \(\Gamma_0(N)\)-optimal |
10830.s2 | 10830t2 | \([1, 1, 1, 249, 573]\) | \(4728305591/3000000\) | \(-1083000000\) | \([]\) | \(7776\) | \(0.42258\) |
Rank
sage: E.rank()
The elliptic curves in class 10830.s have rank \(1\).
Complex multiplication
The elliptic curves in class 10830.s do not have complex multiplication.Modular form 10830.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.