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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 47040ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.hl2 | 47040ds1 | \([0, 1, 0, -240, 1350]\) | \(69934528/225\) | \(4939200\) | \([2]\) | \(16384\) | \(0.15056\) | \(\Gamma_0(N)\)-optimal |
47040.hl1 | 47040ds2 | \([0, 1, 0, -345, -57]\) | \(3241792/1875\) | \(2634240000\) | \([2]\) | \(32768\) | \(0.49713\) |
Rank
sage: E.rank()
The elliptic curves in class 47040ds have rank \(0\).
Complex multiplication
The elliptic curves in class 47040ds do not have complex multiplication.Modular form 47040.2.a.ds
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.