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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 30400.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30400.bl1 | 30400d3 | \([0, 1, 0, -136833, -156757537]\) | \(-69173457625/2550136832\) | \(-10445360463872000000\) | \([]\) | \(497664\) | \(2.3296\) | |
30400.bl2 | 30400d1 | \([0, 1, 0, -24833, 1498463]\) | \(-413493625/152\) | \(-622592000000\) | \([]\) | \(55296\) | \(1.2310\) | \(\Gamma_0(N)\)-optimal |
30400.bl3 | 30400d2 | \([0, 1, 0, 15167, 5730463]\) | \(94196375/3511808\) | \(-14384365568000000\) | \([]\) | \(165888\) | \(1.7803\) |
Rank
sage: E.rank()
The elliptic curves in class 30400.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 30400.bl do not have complex multiplication.Modular form 30400.2.a.bl
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.