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SageMath
E = EllipticCurve("he1")
E.isogeny_class()
Elliptic curves in class 290400he
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 290400.he1 | 290400he1 | \([0, 1, 0, -1628458, 799289588]\) | \(2156689088/81\) | \(17937055125000000\) | \([2]\) | \(5529600\) | \(2.2052\) | \(\Gamma_0(N)\)-optimal |
| 290400.he2 | 290400he2 | \([0, 1, 0, -1552833, 876956463]\) | \(-29218112/6561\) | \(-92985693768000000000\) | \([2]\) | \(11059200\) | \(2.5518\) |
Rank
sage: E.rank()
The elliptic curves in class 290400he have rank \(0\).
Complex multiplication
The elliptic curves in class 290400he do not have complex multiplication.Modular form 290400.2.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.
