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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 145200.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.m1 | 145200jq4 | \([0, -1, 0, -31945008, -69484201488]\) | \(127191074376964/495\) | \(14030763120000000\) | \([2]\) | \(5898240\) | \(2.7345\) | |
| 145200.m2 | 145200jq2 | \([0, -1, 0, -1997508, -1084111488]\) | \(124386546256/245025\) | \(1736306936100000000\) | \([2, 2]\) | \(2949120\) | \(2.3879\) | |
| 145200.m3 | 145200jq3 | \([0, -1, 0, -1332008, -1818823488]\) | \(-9220796644/45106875\) | \(-1278553289310000000000\) | \([2]\) | \(5898240\) | \(2.7345\) | |
| 145200.m4 | 145200jq1 | \([0, -1, 0, -167383, -4337738]\) | \(1171019776/658845\) | \(291796026761250000\) | \([2]\) | \(1474560\) | \(2.0413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145200.m have rank \(0\).
Complex multiplication
The elliptic curves in class 145200.m do not have complex multiplication.Modular form 145200.2.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.
