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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 17160m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17160.f3 | 17160m1 | \([0, -1, 0, -151, 760]\) | \(23955625984/268125\) | \(4290000\) | \([2]\) | \(3584\) | \(0.086607\) | \(\Gamma_0(N)\)-optimal |
17160.f2 | 17160m2 | \([0, -1, 0, -276, -540]\) | \(9115564624/4601025\) | \(1177862400\) | \([2, 2]\) | \(7168\) | \(0.43318\) | |
17160.f1 | 17160m3 | \([0, -1, 0, -3576, -81060]\) | \(4940122601956/4712565\) | \(4825666560\) | \([2]\) | \(14336\) | \(0.77975\) | |
17160.f4 | 17160m4 | \([0, -1, 0, 1024, -5220]\) | \(115850907644/77084865\) | \(-78934901760\) | \([2]\) | \(14336\) | \(0.77975\) |
Rank
sage: E.rank()
The elliptic curves in class 17160m have rank \(1\).
Complex multiplication
The elliptic curves in class 17160m do not have complex multiplication.Modular form 17160.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.