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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 181944ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 181944.bv4 | 181944ce1 | \([0, 0, 0, -14163474, -8036093567]\) | \(572616640141312/280535480757\) | \(153941925076084881399888\) | \([2]\) | \(17694720\) | \(3.1425\) | \(\Gamma_0(N)\)-optimal |
| 181944.bv2 | 181944ce2 | \([0, 0, 0, -120746919, 505120560730]\) | \(22174957026242512/278654127129\) | \(2446552722379747409438976\) | \([2, 2]\) | \(35389440\) | \(3.4891\) | |
| 181944.bv1 | 181944ce3 | \([0, 0, 0, -1926086259, 32535812198878]\) | \(22501000029889239268/3620708343\) | \(127157691074266827168768\) | \([2]\) | \(70778880\) | \(3.8357\) | |
| 181944.bv3 | 181944ce4 | \([0, 0, 0, -20742699, 1316454797590]\) | \(-28104147578308/21301741002339\) | \(-748107813476945816694180864\) | \([2]\) | \(70778880\) | \(3.8357\) |
Rank
sage: E.rank()
The elliptic curves in class 181944ce have rank \(1\).
Complex multiplication
The elliptic curves in class 181944ce do not have complex multiplication.Modular form 181944.2.a.ce
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 Cremona 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 Cremona labels.
