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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 39270.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39270.h1 | 39270h4 | \([1, 1, 0, -54358, 4855312]\) | \(17763420785287316329/530567152500\) | \(530567152500\) | \([2]\) | \(196608\) | \(1.3486\) | |
| 39270.h2 | 39270h3 | \([1, 1, 0, -15438, -676872]\) | \(406949741244540649/41324105079180\) | \(41324105079180\) | \([2]\) | \(196608\) | \(1.3486\) | |
| 39270.h3 | 39270h2 | \([1, 1, 0, -3538, 68068]\) | \(4899919925067049/746392323600\) | \(746392323600\) | \([2, 2]\) | \(98304\) | \(1.0020\) | |
| 39270.h4 | 39270h1 | \([1, 1, 0, 382, 6132]\) | \(6139545014231/18965210880\) | \(-18965210880\) | \([2]\) | \(49152\) | \(0.65544\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39270.h have rank \(1\).
Complex multiplication
The elliptic curves in class 39270.h do not have complex multiplication.Modular form 39270.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
