Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 389376.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 389376.h1 | 389376h4 | \([0, 0, 0, -3938376, 3008308160]\) | \(58591911104/243\) | \(28018433521188864\) | \([2]\) | \(5529600\) | \(2.3654\) | |
| 389376.h2 | 389376h3 | \([0, 0, 0, -242346, 48527336]\) | \(-873722816/59049\) | \(-106382489775763968\) | \([2]\) | \(2764800\) | \(2.0188\) | |
| 389376.h3 | 389376h2 | \([0, 0, 0, -44616, -3515200]\) | \(85184/3\) | \(345906586681344\) | \([2]\) | \(1105920\) | \(1.5606\) | |
| 389376.h4 | 389376h1 | \([0, 0, 0, 1014, -193336]\) | \(64/9\) | \(-16214371250688\) | \([2]\) | \(552960\) | \(1.2141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 389376.h have rank \(0\).
Complex multiplication
The elliptic curves in class 389376.h do not have complex multiplication.Modular form 389376.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
