Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 372232.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372232.d1 | 372232d2 | \([0, 1, 0, -772304, 246970912]\) | \(1030541881826/62236321\) | \(3076574192524593152\) | \([2]\) | \(4915200\) | \(2.3000\) | |
| 372232.d2 | 372232d1 | \([0, 1, 0, -760744, 255136896]\) | \(1969910093092/7889\) | \(194991392605184\) | \([2]\) | \(2457600\) | \(1.9534\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372232.d have rank \(0\).
Complex multiplication
The elliptic curves in class 372232.d do not have complex multiplication.Modular form 372232.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
