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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 48510.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.eh1 | 48510cj3 | \([1, -1, 1, -4733777, 3965414401]\) | \(5066026756449723/11000000\) | \(25472537937000000\) | \([2]\) | \(1492992\) | \(2.3949\) | |
| 48510.eh2 | 48510cj4 | \([1, -1, 1, -4680857, 4058363089]\) | \(-4898016158612283/236328125000\) | \(-547261557240234375000\) | \([2]\) | \(2985984\) | \(2.7414\) | |
| 48510.eh3 | 48510cj1 | \([1, -1, 1, -76817, 1755009]\) | \(15781142246787/8722841600\) | \(27708306967756800\) | \([2]\) | \(497664\) | \(1.8456\) | \(\Gamma_0(N)\)-optimal |
| 48510.eh4 | 48510cj2 | \([1, -1, 1, 299503, 13646721]\) | \(935355271080573/566899520000\) | \(-1800769363968960000\) | \([2]\) | \(995328\) | \(2.1921\) |
Rank
sage: E.rank()
The elliptic curves in class 48510.eh have rank \(1\).
Complex multiplication
The elliptic curves in class 48510.eh do not have complex multiplication.Modular form 48510.2.a.eh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
