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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 131043z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 131043.w3 | 131043z1 | \([1, 1, 0, -66431, -5722944]\) | \(389017/57\) | \(4750644935443737\) | \([2]\) | \(777600\) | \(1.7330\) | \(\Gamma_0(N)\)-optimal |
| 131043.w2 | 131043z2 | \([1, 1, 0, -284836, 52765915]\) | \(30664297/3249\) | \(270786761320293009\) | \([2, 2]\) | \(1555200\) | \(2.0796\) | |
| 131043.w1 | 131043z3 | \([1, 1, 0, -4434531, 3592455750]\) | \(115714886617/1539\) | \(128267413256980899\) | \([2]\) | \(3110400\) | \(2.4262\) | |
| 131043.w4 | 131043z4 | \([1, 1, 0, 370379, 260731156]\) | \(67419143/390963\) | \(-32584673612208592083\) | \([2]\) | \(3110400\) | \(2.4262\) |
Rank
sage: E.rank()
The elliptic curves in class 131043z have rank \(1\).
Complex multiplication
The elliptic curves in class 131043z do not have complex multiplication.Modular form 131043.2.a.z
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 Cremona 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 Cremona labels.
