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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 62400.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.j1 | 62400bm2 | \([0, -1, 0, -5380833, -4803170463]\) | \(-168256703745625/30371328\) | \(-3110023987200000000\) | \([]\) | \(1866240\) | \(2.5522\) | |
62400.j2 | 62400bm1 | \([0, -1, 0, 19167, -22010463]\) | \(7604375/2047032\) | \(-209616076800000000\) | \([]\) | \(622080\) | \(2.0028\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.j have rank \(0\).
Complex multiplication
The elliptic curves in class 62400.j do not have complex multiplication.Modular form 62400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.