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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 145200.fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.fu1 | 145200hm4 | \([0, 1, 0, -654408, -203848812]\) | \(546718898/405\) | \(22959430560000000\) | \([2]\) | \(2211840\) | \(2.0731\) | |
| 145200.fu2 | 145200hm3 | \([0, 1, 0, -412408, 100587188]\) | \(136835858/1875\) | \(106293660000000000\) | \([2]\) | \(2211840\) | \(2.0731\) | |
| 145200.fu3 | 145200hm2 | \([0, 1, 0, -49408, -1778812]\) | \(470596/225\) | \(6377619600000000\) | \([2, 2]\) | \(1105920\) | \(1.7265\) | |
| 145200.fu4 | 145200hm1 | \([0, 1, 0, 11092, -205812]\) | \(21296/15\) | \(-106293660000000\) | \([2]\) | \(552960\) | \(1.3799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145200.fu have rank \(1\).
Complex multiplication
The elliptic curves in class 145200.fu do not have complex multiplication.Modular form 145200.2.a.fu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
