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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 176400.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.s1 | 176400b1 | \([0, 0, 0, -127155, -16892750]\) | \(5177717/189\) | \(8299415996928000\) | \([2]\) | \(1179648\) | \(1.8242\) | \(\Gamma_0(N)\)-optimal |
176400.s2 | 176400b2 | \([0, 0, 0, 49245, -60110750]\) | \(300763/35721\) | \(-1568589623419392000\) | \([2]\) | \(2359296\) | \(2.1708\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.s have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.s do not have complex multiplication.Modular form 176400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.