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SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 394944fx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 394944.fx4 | 394944fx1 | \([0, 1, 0, -45279329, -91724697825]\) | \(22106889268753393/4969545596928\) | \(2307877284672795995799552\) | \([2]\) | \(61931520\) | \(3.3878\) | \(\Gamma_0(N)\)-optimal |
| 394944.fx2 | 394944fx2 | \([0, 1, 0, -679667809, -6819922039009]\) | \(74768347616680342513/5615307472896\) | \(2607771738961637711806464\) | \([2, 2]\) | \(123863040\) | \(3.7344\) | |
| 394944.fx3 | 394944fx3 | \([0, 1, 0, -635062369, -7753665556705]\) | \(-60992553706117024753/20624795251201152\) | \(-9578239203741050873648775168\) | \([2]\) | \(247726080\) | \(4.0809\) | |
| 394944.fx1 | 394944fx4 | \([0, 1, 0, -10874488929, -436480658141409]\) | \(306234591284035366263793/1727485056\) | \(802251119864687099904\) | \([2]\) | \(247726080\) | \(4.0809\) |
Rank
sage: E.rank()
The elliptic curves in class 394944fx have rank \(0\).
Complex multiplication
The elliptic curves in class 394944fx do not have complex multiplication.Modular form 394944.2.a.fx
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.
