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SageMath
sage: E = EllipticCurve("fu1")
sage: E.isogeny_class()
Elliptic curves in class 227430.fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
227430.fu1 | 227430h7 | [1, -1, 1, -20959367, 23241143409] | [2] | 31850496 | |
227430.fu2 | 227430h4 | [1, -1, 1, -18717557, 31173602901] | [2] | 10616832 | |
227430.fu3 | 227430h6 | [1, -1, 1, -8775617, -9737831091] | [2, 2] | 15925248 | |
227430.fu4 | 227430h3 | [1, -1, 1, -8710637, -9892977339] | [2] | 7962624 | |
227430.fu5 | 227430h2 | [1, -1, 1, -1172957, 484588581] | [2, 2] | 5308416 | |
227430.fu6 | 227430h5 | [1, -1, 1, -263237, 1216367349] | [2] | 10616832 | |
227430.fu7 | 227430h1 | [1, -1, 1, -133277, -6556251] | [2] | 2654208 | \(\Gamma_0(N)\)-optimal |
227430.fu8 | 227430h8 | [1, -1, 1, 2368453, -32788225479] | [2] | 31850496 |
Rank
sage: E.rank()
The elliptic curves in class 227430.fu have rank \(0\).
Complex multiplication
The elliptic curves in class 227430.fu do not have complex multiplication.Modular form 227430.2.a.fu
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.