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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 37030.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37030.j1 | 37030j2 | \([1, -1, 0, -8257789, 9134645445]\) | \(420676324562824569/56350000000\) | \(8341822345150000000\) | \([2]\) | \(1419264\) | \(2.6497\) | |
37030.j2 | 37030j1 | \([1, -1, 0, -470909, 168831813]\) | \(-78013216986489/37918720000\) | \(-5613331424942080000\) | \([2]\) | \(709632\) | \(2.3031\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37030.j have rank \(0\).
Complex multiplication
The elliptic curves in class 37030.j do not have complex multiplication.Modular form 37030.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.