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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 57960.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.c1 | 57960bn4 | \([0, 0, 0, -350283, 79364518]\) | \(3183636045638162/19833730875\) | \(29611601526528000\) | \([2]\) | \(786432\) | \(1.9984\) | |
| 57960.c2 | 57960bn2 | \([0, 0, 0, -35283, -456482]\) | \(6507178816324/3645140625\) | \(2721082896000000\) | \([2, 2]\) | \(393216\) | \(1.6519\) | |
| 57960.c3 | 57960bn1 | \([0, 0, 0, -26463, -1654238]\) | \(10981797946576/20708625\) | \(3864726432000\) | \([2]\) | \(196608\) | \(1.3053\) | \(\Gamma_0(N)\)-optimal |
| 57960.c4 | 57960bn3 | \([0, 0, 0, 138597, -3621098]\) | \(197209449637198/117919921875\) | \(-176053500000000000\) | \([2]\) | \(786432\) | \(1.9984\) |
Rank
sage: E.rank()
The elliptic curves in class 57960.c have rank \(1\).
Complex multiplication
The elliptic curves in class 57960.c do not have complex multiplication.Modular form 57960.2.a.c
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.
