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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 271062.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271062.d1 | 271062d4 | \([1, -1, 0, -69089102163, -6989745509872331]\) | \(19499096390516434897995817/15393430272\) | \(28792095988424460417792\) | \([2]\) | \(672399360\) | \(4.5141\) | |
| 271062.d2 | 271062d2 | \([1, -1, 0, -4318098003, -109212417361355]\) | \(4760617885089919932457/133756441657344\) | \(250179994921170002376720384\) | \([2, 2]\) | \(336199680\) | \(4.1675\) | |
| 271062.d3 | 271062d3 | \([1, -1, 0, -4144618323, -118389665913035]\) | \(-4209586785160189454377/801182513521564416\) | \(-1498543432227661234168753502976\) | \([2]\) | \(672399360\) | \(4.5141\) | |
| 271062.d4 | 271062d1 | \([1, -1, 0, -280752723, -1561450284491]\) | \(1308451928740468777/194033737531392\) | \(362923526288903585358938112\) | \([2]\) | \(168099840\) | \(3.8209\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271062.d have rank \(0\).
Complex multiplication
The elliptic curves in class 271062.d do not have complex multiplication.Modular form 271062.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
