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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 207214.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207214.s1 | 207214d2 | \([1, 0, 0, -261552, 50914432]\) | \(42060685455433/516618368\) | \(24304766263342208\) | \([2]\) | \(2935296\) | \(1.9544\) | |
207214.s2 | 207214d1 | \([1, 0, 0, -30512, -792320]\) | \(66775173193/32915456\) | \(1548536626036736\) | \([2]\) | \(1467648\) | \(1.6078\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 207214.s have rank \(1\).
Complex multiplication
The elliptic curves in class 207214.s do not have complex multiplication.Modular form 207214.2.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.