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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 112632.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112632.b1 | 112632d1 | \([0, -1, 0, -1140880, 469004956]\) | \(497005996/507\) | \(167529126680527872\) | \([2]\) | \(4012800\) | \(2.2235\) | \(\Gamma_0(N)\)-optimal |
| 112632.b2 | 112632d2 | \([0, -1, 0, -866520, 700016076]\) | \(-108879878/257049\) | \(-169874534454055262208\) | \([2]\) | \(8025600\) | \(2.5701\) |
Rank
sage: E.rank()
The elliptic curves in class 112632.b have rank \(0\).
Complex multiplication
The elliptic curves in class 112632.b do not have complex multiplication.Modular form 112632.2.a.b
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.
