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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 44400.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44400.co1 | 44400n4 | \([0, 1, 0, -64408, 6141188]\) | \(1846842725956/43359375\) | \(693750000000000\) | \([2]\) | \(172032\) | \(1.6333\) | |
| 44400.co2 | 44400n2 | \([0, 1, 0, -8908, -185812]\) | \(19545784144/7700625\) | \(30802500000000\) | \([2, 2]\) | \(86016\) | \(1.2867\) | |
| 44400.co3 | 44400n1 | \([0, 1, 0, -7783, -266812]\) | \(208583809024/74925\) | \(18731250000\) | \([2]\) | \(43008\) | \(0.94014\) | \(\Gamma_0(N)\)-optimal |
| 44400.co4 | 44400n3 | \([0, 1, 0, 28592, -1310812]\) | \(161555647964/140562075\) | \(-2248993200000000\) | \([2]\) | \(172032\) | \(1.6333\) |
Rank
sage: E.rank()
The elliptic curves in class 44400.co have rank \(0\).
Complex multiplication
The elliptic curves in class 44400.co do not have complex multiplication.Modular form 44400.2.a.co
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.
