Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1456.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1456.d1 | 1456g3 | \([0, -1, 0, -250608, 48371776]\) | \(-424962187484640625/182\) | \(-745472\) | \([]\) | \(2592\) | \(1.3736\) | |
| 1456.d2 | 1456g2 | \([0, -1, 0, -3088, 67520]\) | \(-795309684625/6028568\) | \(-24693014528\) | \([]\) | \(864\) | \(0.82430\) | |
| 1456.d3 | 1456g1 | \([0, -1, 0, 112, 448]\) | \(37595375/46592\) | \(-190840832\) | \([]\) | \(288\) | \(0.27499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1456.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1456.d do not have complex multiplication.Modular form 1456.2.a.d
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
