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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4620.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4620.h1 | 4620h2 | \([0, 1, 0, -1449196, -671887996]\) | \(1314817350433665559504/190690249278375\) | \(48816703815264000\) | \([2]\) | \(80640\) | \(2.2172\) | |
| 4620.h2 | 4620h1 | \([0, 1, 0, -82321, -12507496]\) | \(-3856034557002072064/1973796785296875\) | \(-31580748564750000\) | \([2]\) | \(40320\) | \(1.8706\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4620.h have rank \(1\).
Complex multiplication
The elliptic curves in class 4620.h do not have complex multiplication.Modular form 4620.2.a.h
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.
