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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 80688.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80688.ba1 | 80688bc1 | \([0, 1, 0, -12208000824, 519172310165076]\) | \(10341755683137709164937/356992303104\) | \(6945794674600623571206144\) | \([2]\) | \(67737600\) | \(4.2643\) | \(\Gamma_0(N)\)-optimal |
| 80688.ba2 | 80688bc2 | \([0, 1, 0, -12190787384, 520709394617940]\) | \(-10298071306410575356297/60769798505543808\) | \(-1182363146673762731589999525888\) | \([2]\) | \(135475200\) | \(4.6109\) |
Rank
sage: E.rank()
The elliptic curves in class 80688.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 80688.ba do not have complex multiplication.Modular form 80688.2.a.ba
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.
