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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 279312.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 279312.w1 | 279312w1 | \([0, -1, 0, -4408, 34816]\) | \(62500/33\) | \(5002428761088\) | \([2]\) | \(402688\) | \(1.1283\) | \(\Gamma_0(N)\)-optimal |
| 279312.w2 | 279312w2 | \([0, -1, 0, 16752, 254880]\) | \(1714750/1089\) | \(-330160298231808\) | \([2]\) | \(805376\) | \(1.4749\) |
Rank
sage: E.rank()
The elliptic curves in class 279312.w have rank \(1\).
Complex multiplication
The elliptic curves in class 279312.w do not have complex multiplication.Modular form 279312.2.a.w
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.
