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SageMath
E = EllipticCurve("ha1")
E.isogeny_class()
Elliptic curves in class 145200.ha
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.ha1 | 145200ht1 | \([0, 1, 0, -25208, 447588]\) | \(62500/33\) | \(935384208000000\) | \([2]\) | \(552960\) | \(1.5642\) | \(\Gamma_0(N)\)-optimal |
| 145200.ha2 | 145200ht2 | \([0, 1, 0, 95792, 3593588]\) | \(1714750/1089\) | \(-61735357728000000\) | \([2]\) | \(1105920\) | \(1.9108\) |
Rank
sage: E.rank()
The elliptic curves in class 145200.ha have rank \(1\).
Complex multiplication
The elliptic curves in class 145200.ha do not have complex multiplication.Modular form 145200.2.a.ha
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 LMFDB 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 LMFDB labels.
