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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 271440d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271440.d2 | 271440d1 | \([0, 0, 0, -31563, -78661638]\) | \(-43132764843/33130760000\) | \(-2671053820231680000\) | \([2]\) | \(3760128\) | \(2.2148\) | \(\Gamma_0(N)\)-optimal |
| 271440.d1 | 271440d2 | \([0, 0, 0, -2951883, -1930728582]\) | \(35283356390293803/444153125000\) | \(35808321369600000000\) | \([2]\) | \(7520256\) | \(2.5614\) |
Rank
sage: E.rank()
The elliptic curves in class 271440d have rank \(0\).
Complex multiplication
The elliptic curves in class 271440d do not have complex multiplication.Modular form 271440.2.a.d
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 Cremona 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 Cremona labels.
