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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 302016.fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.fl1 | 302016fl4 | \([0, 1, 0, -504719233, -4364098531201]\) | \(30618029936661765625/3678951124992\) | \(1708519937524879199305728\) | \([2]\) | \(79626240\) | \(3.6745\) | |
| 302016.fl2 | 302016fl3 | \([0, 1, 0, -28927873, -79977967489]\) | \(-5764706497797625/2612665516032\) | \(-1213332543044889071321088\) | \([2]\) | \(39813120\) | \(3.3279\) | |
| 302016.fl3 | 302016fl2 | \([0, 1, 0, -13943233, 11412933695]\) | \(645532578015625/252306960048\) | \(117172383370338612805632\) | \([2]\) | \(26542080\) | \(3.1252\) | |
| 302016.fl4 | 302016fl1 | \([0, 1, 0, 2783807, 1286383679]\) | \(5137417856375/4510142208\) | \(-2094528473372213379072\) | \([2]\) | \(13271040\) | \(2.7786\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.fl have rank \(1\).
Complex multiplication
The elliptic curves in class 302016.fl do not have complex multiplication.Modular form 302016.2.a.fl
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.
