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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 101400g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.m2 | 101400g1 | \([0, -1, 0, -1408, 13202812]\) | \(-4/975\) | \(-75298220400000000\) | \([2]\) | \(774144\) | \(1.9172\) | \(\Gamma_0(N)\)-optimal |
| 101400.m1 | 101400g2 | \([0, -1, 0, -846408, 295432812]\) | \(434163602/7605\) | \(1174652238240000000\) | \([2]\) | \(1548288\) | \(2.2638\) |
Rank
sage: E.rank()
The elliptic curves in class 101400g have rank \(1\).
Complex multiplication
The elliptic curves in class 101400g do not have complex multiplication.Modular form 101400.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
