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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4056.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4056.m1 | 4056f3 | \([0, 1, 0, -140664, -20352864]\) | \(62275269892/39\) | \(192763444224\) | \([2]\) | \(10752\) | \(1.4856\) | |
| 4056.m2 | 4056f2 | \([0, 1, 0, -8844, -316224]\) | \(61918288/1521\) | \(1879443581184\) | \([2, 2]\) | \(5376\) | \(1.1390\) | |
| 4056.m3 | 4056f1 | \([0, 1, 0, -1239, 9270]\) | \(2725888/1053\) | \(81322078032\) | \([4]\) | \(2688\) | \(0.79245\) | \(\Gamma_0(N)\)-optimal |
| 4056.m4 | 4056f4 | \([0, 1, 0, 1296, -989520]\) | \(48668/85683\) | \(-423501286960128\) | \([2]\) | \(10752\) | \(1.4856\) |
Rank
sage: E.rank()
The elliptic curves in class 4056.m have rank \(0\).
Complex multiplication
The elliptic curves in class 4056.m do not have complex multiplication.Modular form 4056.2.a.m
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.
