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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 301665.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301665.j1 | 301665j4 | \([1, 1, 1, -17043217786, -291673983972142]\) | \(113427504990295422838963508521/58027180209113067464728125\) | \(280086115677968836056356896303125\) | \([2]\) | \(1083801600\) | \(4.9183\) | |
| 301665.j2 | 301665j2 | \([1, 1, 1, -9456702161, 350709674665358]\) | \(19376830118286544051859258521/204924651376739150390625\) | \(989132151587106921757822265625\) | \([2, 2]\) | \(541900800\) | \(4.5718\) | |
| 301665.j3 | 301665j1 | \([1, 1, 1, -9432568116, 352604747454084]\) | \(19228856062423570773425497801/2185029055063115625\) | \(10546717908240142066790625\) | \([2]\) | \(270950400\) | \(4.2252\) | \(\Gamma_0(N)\)-optimal |
| 301665.j4 | 301665j3 | \([1, 1, 1, -2256331256, 871809157505294]\) | \(-263191692508335916938917641/67872513354206085205078125\) | \(-327607658310702119922637939453125\) | \([2]\) | \(1083801600\) | \(4.9183\) |
Rank
sage: E.rank()
The elliptic curves in class 301665.j have rank \(1\).
Complex multiplication
The elliptic curves in class 301665.j do not have complex multiplication.Modular form 301665.2.a.j
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.
