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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 121680.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121680.p1 | 121680bc1 | \([0, 0, 0, -88569858, 285543252943]\) | \(621217777580032/74733890625\) | \(9243900748547670143250000\) | \([2]\) | \(23482368\) | \(3.5212\) | \(\Gamma_0(N)\)-optimal |
| 121680.p2 | 121680bc2 | \([0, 0, 0, 127647897, 1462157032102]\) | \(116227003261808/533935546875\) | \(-1056687328366217437500000000\) | \([2]\) | \(46964736\) | \(3.8678\) |
Rank
sage: E.rank()
The elliptic curves in class 121680.p have rank \(1\).
Complex multiplication
The elliptic curves in class 121680.p do not have complex multiplication.Modular form 121680.2.a.p
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.
