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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 344760.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.cl1 | 344760cl4 | \([0, 1, 0, -5525680, -5001293920]\) | \(1887517194957938/21849165\) | \(215985656349665280\) | \([2]\) | \(8257536\) | \(2.4773\) | |
| 344760.cl2 | 344760cl2 | \([0, 1, 0, -354280, -73984000]\) | \(994958062276/98903025\) | \(488843275465958400\) | \([2, 2]\) | \(4128768\) | \(2.1308\) | |
| 344760.cl3 | 344760cl1 | \([0, 1, 0, -80500, 7492928]\) | \(46689225424/7249905\) | \(8958440116005120\) | \([4]\) | \(2064384\) | \(1.7842\) | \(\Gamma_0(N)\)-optimal |
| 344760.cl4 | 344760cl3 | \([0, 1, 0, 436640, -356816992]\) | \(931329171502/6107473125\) | \(-60374233593872640000\) | \([2]\) | \(8257536\) | \(2.4773\) |
Rank
sage: E.rank()
The elliptic curves in class 344760.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 344760.cl do not have complex multiplication.Modular form 344760.2.a.cl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
