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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 8820.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8820.h1 | 8820a4 | \([0, 0, 0, -186543, 12428262]\) | \(1210991472/588245\) | \(348720711650922240\) | \([2]\) | \(82944\) | \(2.0596\) | |
| 8820.h2 | 8820a3 | \([0, 0, 0, -153468, 23124717]\) | \(10788913152/8575\) | \(317712018632400\) | \([2]\) | \(41472\) | \(1.7130\) | |
| 8820.h3 | 8820a2 | \([0, 0, 0, -98343, -11869858]\) | \(129348709488/6125\) | \(4980788064000\) | \([2]\) | \(27648\) | \(1.5103\) | |
| 8820.h4 | 8820a1 | \([0, 0, 0, -6468, -164983]\) | \(588791808/109375\) | \(5558915250000\) | \([2]\) | \(13824\) | \(1.1637\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8820.h have rank \(1\).
Complex multiplication
The elliptic curves in class 8820.h do not have complex multiplication.Modular form 8820.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
