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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 7056.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7056.bp1 | 7056bm2 | \([0, 0, 0, -6437424, -6291657232]\) | \(-1713910976512/1594323\) | \(-27444044051345682432\) | \([]\) | \(174720\) | \(2.6528\) | |
7056.bp2 | 7056bm1 | \([0, 0, 0, -16464, 883568]\) | \(-28672/3\) | \(-51640810647552\) | \([]\) | \(13440\) | \(1.3703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.bp do not have complex multiplication.Modular form 7056.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.