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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 83790.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.dn1 | 83790ed4 | \([1, -1, 1, -543948593, -4882827122463]\) | \(207530301091125281552569/805586668007040\) | \(69092043644278621491840\) | \([2]\) | \(20643840\) | \(3.5957\) | |
| 83790.dn2 | 83790ed3 | \([1, -1, 1, -103089713, 311090413281]\) | \(1412712966892699019449/330160465517040000\) | \(28316582434950780201840000\) | \([2]\) | \(20643840\) | \(3.5957\) | |
| 83790.dn3 | 83790ed2 | \([1, -1, 1, -34505393, -73887091743]\) | \(52974743974734147769/3152005008998400\) | \(270335242994362863206400\) | \([2, 2]\) | \(10321920\) | \(3.2491\) | |
| 83790.dn4 | 83790ed1 | \([1, -1, 1, 1621327, -4769451039]\) | \(5495662324535111/117739817533440\) | \(-10098087437090936586240\) | \([2]\) | \(5160960\) | \(2.9025\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 83790.dn do not have complex multiplication.Modular form 83790.2.a.dn
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
