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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 270480.en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.en1 | 270480en4 | \([0, -1, 0, -3520960, -2541736448]\) | \(10017490085065009/235066440\) | \(113276238231797760\) | \([2]\) | \(7077888\) | \(2.3844\) | |
| 270480.en2 | 270480en3 | \([0, -1, 0, -949440, 319449600]\) | \(196416765680689/22365315000\) | \(10777628444405760000\) | \([2]\) | \(7077888\) | \(2.3844\) | |
| 270480.en3 | 270480en2 | \([0, -1, 0, -228160, -36574208]\) | \(2725812332209/373262400\) | \(179871531407769600\) | \([2, 2]\) | \(3538944\) | \(2.0378\) | |
| 270480.en4 | 270480en1 | \([0, -1, 0, 22720, -3056640]\) | \(2691419471/9891840\) | \(-4766781784719360\) | \([2]\) | \(1769472\) | \(1.6912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270480.en have rank \(1\).
Complex multiplication
The elliptic curves in class 270480.en do not have complex multiplication.Modular form 270480.2.a.en
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.
