Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 1152.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1152.r1 | 1152f2 | \([0, 0, 0, -84, 272]\) | \(10976\) | \(5971968\) | \([2]\) | \(192\) | \(0.039450\) | |
1152.r2 | 1152f1 | \([0, 0, 0, 6, 20]\) | \(128\) | \(-186624\) | \([2]\) | \(96\) | \(-0.30712\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1152.r have rank \(0\).
Complex multiplication
The elliptic curves in class 1152.r do not have complex multiplication.Modular form 1152.2.a.r
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.