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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 126925.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126925.a1 | 126925a2 | \([0, -1, 1, -2288883, -1330983957]\) | \(84873997297419452416/81790244708125\) | \(1277972573564453125\) | \([]\) | \(1928448\) | \(2.3955\) | |
| 126925.a2 | 126925a1 | \([0, -1, 1, -101383, 10500418]\) | \(7375702385852416/1239501953125\) | \(19367218017578125\) | \([]\) | \(642816\) | \(1.8462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126925.a have rank \(1\).
Complex multiplication
The elliptic curves in class 126925.a do not have complex multiplication.Modular form 126925.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
