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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 34650.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34650.dd1 | 34650cx4 | \([1, -1, 1, -3179930, 2183242947]\) | \(312196988566716625/25367712678\) | \(288954102222843750\) | \([2]\) | \(663552\) | \(2.3956\) | |
| 34650.dd2 | 34650cx3 | \([1, -1, 1, -185180, 39001947]\) | \(-61653281712625/21875235228\) | \(-249172601268937500\) | \([2]\) | \(331776\) | \(2.0490\) | |
| 34650.dd3 | 34650cx2 | \([1, -1, 1, -81680, -4486053]\) | \(5290763640625/2291573592\) | \(26102455446375000\) | \([2]\) | \(221184\) | \(1.8463\) | |
| 34650.dd4 | 34650cx1 | \([1, -1, 1, 17320, -526053]\) | \(50447927375/39517632\) | \(-450130527000000\) | \([2]\) | \(110592\) | \(1.4997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34650.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 34650.dd do not have complex multiplication.Modular form 34650.2.a.dd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
