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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 62400.fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.fn1 | 62400ha4 | \([0, 1, 0, -171149633, -667049887137]\) | \(1082883335268084577352/251301565117746585\) | \(128666401340286251520000000\) | \([4]\) | \(20643840\) | \(3.7220\) | |
| 62400.fn2 | 62400ha2 | \([0, 1, 0, -160164633, -780184402137]\) | \(7099759044484031233216/577161945398025\) | \(36938364505473600000000\) | \([2, 2]\) | \(10321920\) | \(3.3754\) | |
| 62400.fn3 | 62400ha1 | \([0, 1, 0, -160161508, -780216367762]\) | \(454357982636417669333824/3003024375\) | \(3003024375000000\) | \([2]\) | \(5160960\) | \(3.0289\) | \(\Gamma_0(N)\)-optimal |
| 62400.fn4 | 62400ha3 | \([0, 1, 0, -149229633, -891273067137]\) | \(-717825640026599866952/254764560814329735\) | \(-130439455136936824320000000\) | \([2]\) | \(20643840\) | \(3.7220\) |
Rank
sage: E.rank()
The elliptic curves in class 62400.fn have rank \(0\).
Complex multiplication
The elliptic curves in class 62400.fn do not have complex multiplication.Modular form 62400.2.a.fn
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.
