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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 36784bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36784.j2 | 36784bh1 | \([0, -1, 0, -30048, 2015488]\) | \(-413493625/152\) | \(-1102959706112\) | \([]\) | \(51840\) | \(1.2787\) | \(\Gamma_0(N)\)-optimal |
36784.j3 | 36784bh2 | \([0, -1, 0, 18352, 7614400]\) | \(94196375/3511808\) | \(-25482781050011648\) | \([]\) | \(155520\) | \(1.8280\) | |
36784.j1 | 36784bh3 | \([0, -1, 0, -165568, -208528384]\) | \(-69173457625/2550136832\) | \(-18504593228737544192\) | \([]\) | \(466560\) | \(2.3773\) |
Rank
sage: E.rank()
The elliptic curves in class 36784bh have rank \(2\).
Complex multiplication
The elliptic curves in class 36784bh do not have complex multiplication.Modular form 36784.2.a.bh
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.