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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 41280di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.do1 | 41280di1 | \([0, 1, 0, -12225, -483777]\) | \(770842973809/66873600\) | \(17530512998400\) | \([2]\) | \(122880\) | \(1.2820\) | \(\Gamma_0(N)\)-optimal |
41280.do2 | 41280di2 | \([0, 1, 0, 13375, -2219457]\) | \(1009328859791/8734528080\) | \(-2289704129003520\) | \([2]\) | \(245760\) | \(1.6286\) |
Rank
sage: E.rank()
The elliptic curves in class 41280di have rank \(0\).
Complex multiplication
The elliptic curves in class 41280di do not have complex multiplication.Modular form 41280.2.a.di
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.