Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 144400t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 144400.bj2 | 144400t1 | \([0, 0, 0, 1805, 1028850]\) | \(27/19\) | \(-457662330368000\) | \([2]\) | \(368640\) | \(1.4921\) | \(\Gamma_0(N)\)-optimal |
| 144400.bj1 | 144400t2 | \([0, 0, 0, -142595, 20234050]\) | \(13312053/361\) | \(8695584276992000\) | \([2]\) | \(737280\) | \(1.8387\) |
Rank
sage: E.rank()
The elliptic curves in class 144400t have rank \(0\).
Complex multiplication
The elliptic curves in class 144400t do not have complex multiplication.Modular form 144400.2.a.t
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
