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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 308898d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308898.d4 | 308898d1 | \([1, -1, 0, -4559463, 561265789]\) | \(2845178713/1609728\) | \(5930725187981613699072\) | \([2]\) | \(19768320\) | \(2.8678\) | \(\Gamma_0(N)\)-optimal |
| 308898.d2 | 308898d2 | \([1, -1, 0, -53983143, 152400695485]\) | \(4722184089433/9884736\) | \(36418359357449596620864\) | \([2, 2]\) | \(39536640\) | \(3.2144\) | |
| 308898.d1 | 308898d3 | \([1, -1, 0, -863295903, 9763313445589]\) | \(19312898130234073/84888\) | \(312753086084967909912\) | \([2]\) | \(79073280\) | \(3.5610\) | |
| 308898.d3 | 308898d4 | \([1, -1, 0, -35449263, 258618361765]\) | \(-1337180541913/7067998104\) | \(-26040644372216355317110296\) | \([2]\) | \(79073280\) | \(3.5610\) |
Rank
sage: E.rank()
The elliptic curves in class 308898d have rank \(1\).
Complex multiplication
The elliptic curves in class 308898d do not have complex multiplication.Modular form 308898.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
