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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 46090i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46090.p1 | 46090i1 | \([1, -1, 1, -93, -319]\) | \(88061730849/460900\) | \(460900\) | \([2]\) | \(6048\) | \(-0.068075\) | \(\Gamma_0(N)\)-optimal |
46090.p2 | 46090i2 | \([1, -1, 1, -43, -699]\) | \(-8602523649/212428810\) | \(-212428810\) | \([2]\) | \(12096\) | \(0.27850\) |
Rank
sage: E.rank()
The elliptic curves in class 46090i have rank \(1\).
Complex multiplication
The elliptic curves in class 46090i do not have complex multiplication.Modular form 46090.2.a.i
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.