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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 371280fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.fk4 | 371280fk1 | \([0, 1, 0, -5320, 10289780]\) | \(-4066120948681/11168482590720\) | \(-45746104691589120\) | \([2]\) | \(2949120\) | \(1.8758\) | \(\Gamma_0(N)\)-optimal |
| 371280.fk3 | 371280fk2 | \([0, 1, 0, -742600, 242975348]\) | \(11056793118237203401/159353257190400\) | \(652710941451878400\) | \([2, 2]\) | \(5898240\) | \(2.2223\) | |
| 371280.fk1 | 371280fk3 | \([0, 1, 0, -11840200, 15677517428]\) | \(44816807438220995641801/9512718589920\) | \(38964095344312320\) | \([2]\) | \(11796480\) | \(2.5689\) | |
| 371280.fk2 | 371280fk4 | \([0, 1, 0, -1441480, -287893900]\) | \(80870462846141298121/38087635627860000\) | \(156006955531714560000\) | \([2]\) | \(11796480\) | \(2.5689\) |
Rank
sage: E.rank()
The elliptic curves in class 371280fk have rank \(0\).
Complex multiplication
The elliptic curves in class 371280fk do not have complex multiplication.Modular form 371280.2.a.fk
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.
