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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8820.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8820.o1 | 8820q2 | \([0, 0, 0, -13503, 382102]\) | \(4253563312/1476225\) | \(94496161939200\) | \([2]\) | \(30720\) | \(1.3833\) | |
| 8820.o2 | 8820q1 | \([0, 0, 0, -5628, -158123]\) | \(4927700992/151875\) | \(607614210000\) | \([2]\) | \(15360\) | \(1.0367\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8820.o have rank \(0\).
Complex multiplication
The elliptic curves in class 8820.o do not have complex multiplication.Modular form 8820.2.a.o
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.
