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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 363090d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363090.d2 | 363090d1 | \([1, 1, 0, -8478783723, 302240513182077]\) | \(-572975621510210833793129957161/3853924401600000000000000\) | \(-453410351923838400000000000000\) | \([2]\) | \(877879296\) | \(4.5256\) | \(\Gamma_0(N)\)-optimal |
363090.d1 | 363090d2 | \([1, 1, 0, -135878783723, 19278546953182077]\) | \(2358253156081889555517943529957161/105632206512061320000000\) | \(12427523463937502236680000000\) | \([2]\) | \(1755758592\) | \(4.8722\) |
Rank
sage: E.rank()
The elliptic curves in class 363090d have rank \(1\).
Complex multiplication
The elliptic curves in class 363090d do not have complex multiplication.Modular form 363090.2.a.d
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.