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SageMath
E = EllipticCurve("he1")
E.isogeny_class()
Elliptic curves in class 338800he
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338800.he2 | 338800he1 | \([0, -1, 0, 11578692, 16071946112]\) | \(24226243449392/29774625727\) | \(-210990262910199388000000\) | \([2]\) | \(29491200\) | \(3.1616\) | \(\Gamma_0(N)\)-optimal |
338800.he1 | 338800he2 | \([0, -1, 0, -68946808, 154575806112]\) | \(1278763167594532/375974556419\) | \(10656989778307200944000000\) | \([2]\) | \(58982400\) | \(3.5082\) |
Rank
sage: E.rank()
The elliptic curves in class 338800he have rank \(0\).
Complex multiplication
The elliptic curves in class 338800he do not have complex multiplication.Modular form 338800.2.a.he
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.