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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 7840.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7840.w1 | 7840n1 | \([0, -1, 0, -310, -1980]\) | \(438976/5\) | \(37647680\) | \([2]\) | \(2880\) | \(0.26691\) | \(\Gamma_0(N)\)-optimal |
| 7840.w2 | 7840n2 | \([0, -1, 0, -65, -5263]\) | \(-64/25\) | \(-12047257600\) | \([2]\) | \(5760\) | \(0.61348\) |
Rank
sage: E.rank()
The elliptic curves in class 7840.w have rank \(1\).
Complex multiplication
The elliptic curves in class 7840.w do not have complex multiplication.Modular form 7840.2.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.
