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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 270400v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270400.v2 | 270400v1 | \([0, 1, 0, -8793633, 9974540863]\) | \(3803721481/26000\) | \(514035851264000000000\) | \([2]\) | \(18579456\) | \(2.8081\) | \(\Gamma_0(N)\)-optimal |
| 270400.v3 | 270400v2 | \([0, 1, 0, -3385633, 22115500863]\) | \(-217081801/10562500\) | \(-208827064576000000000000\) | \([2]\) | \(37158912\) | \(3.1546\) | |
| 270400.v1 | 270400v3 | \([0, 1, 0, -56113633, -155314219137]\) | \(988345570681/44994560\) | \(889569882763427840000000\) | \([2]\) | \(55738368\) | \(3.3574\) | |
| 270400.v4 | 270400v4 | \([0, 1, 0, 30414367, -590982699137]\) | \(157376536199/7722894400\) | \(-152686330658691481600000000\) | \([2]\) | \(111476736\) | \(3.7039\) |
Rank
sage: E.rank()
The elliptic curves in class 270400v have rank \(1\).
Complex multiplication
The elliptic curves in class 270400v do not have complex multiplication.Modular form 270400.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
