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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4840h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4840.e3 | 4840h1 | \([0, 0, 0, -610082, -183413131]\) | \(885956203616256/15125\) | \(428717762000\) | \([2]\) | \(34560\) | \(1.7739\) | \(\Gamma_0(N)\)-optimal |
| 4840.e2 | 4840h2 | \([0, 0, 0, -610687, -183031134]\) | \(55537159171536/228765625\) | \(103749698404000000\) | \([2, 2]\) | \(69120\) | \(2.1205\) | |
| 4840.e1 | 4840h3 | \([0, 0, 0, -913187, 17284366]\) | \(46424454082884/26794860125\) | \(48607978698654848000\) | \([2]\) | \(138240\) | \(2.4671\) | |
| 4840.e4 | 4840h4 | \([0, 0, 0, -317867, -358898826]\) | \(-1957960715364/29541015625\) | \(-53589720250000000000\) | \([2]\) | \(138240\) | \(2.4671\) |
Rank
sage: E.rank()
The elliptic curves in class 4840h have rank \(0\).
Complex multiplication
The elliptic curves in class 4840h do not have complex multiplication.Modular form 4840.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
