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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 179520dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.n2 | 179520dp1 | \([0, -1, 0, -743841, 245943105]\) | \(173629978755828841/1000026931200\) | \(262151059852492800\) | \([2]\) | \(2703360\) | \(2.1834\) | \(\Gamma_0(N)\)-optimal |
179520.n1 | 179520dp2 | \([0, -1, 0, -11884961, 15774436161]\) | \(708234550511150304361/23696640000\) | \(6211931996160000\) | \([2]\) | \(5406720\) | \(2.5300\) |
Rank
sage: E.rank()
The elliptic curves in class 179520dp have rank \(0\).
Complex multiplication
The elliptic curves in class 179520dp do not have complex multiplication.Modular form 179520.2.a.dp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.