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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 27456.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27456.n1 | 27456n4 | \([0, -1, 0, -4171233, -3277295007]\) | \(30618029936661765625/3678951124992\) | \(964414963709902848\) | \([2]\) | \(663552\) | \(2.4755\) | |
| 27456.n2 | 27456n3 | \([0, -1, 0, -239073, -60001695]\) | \(-5764706497797625/2612665516032\) | \(-684894589034692608\) | \([2]\) | \(331776\) | \(2.1290\) | |
| 27456.n3 | 27456n2 | \([0, -1, 0, -115233, 8616609]\) | \(645532578015625/252306960048\) | \(66140755734822912\) | \([2]\) | \(221184\) | \(1.9262\) | |
| 27456.n4 | 27456n1 | \([0, -1, 0, 23007, 958113]\) | \(5137417856375/4510142208\) | \(-1182306718973952\) | \([2]\) | \(110592\) | \(1.5797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27456.n have rank \(0\).
Complex multiplication
The elliptic curves in class 27456.n do not have complex multiplication.Modular form 27456.2.a.n
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.
