Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 152592.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.t1 | 152592bx1 | \([0, -1, 0, -5808, 169920]\) | \(1076890625/17424\) | \(350634442752\) | \([2]\) | \(147456\) | \(1.0148\) | \(\Gamma_0(N)\)-optimal |
152592.t2 | 152592bx2 | \([0, -1, 0, -368, 470208]\) | \(-274625/4743684\) | \(-95460227039232\) | \([2]\) | \(294912\) | \(1.3614\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.t have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.t do not have complex multiplication.Modular form 152592.2.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 LMFDB 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 LMFDB labels.