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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 310464.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.bh1 | 310464bh2 | \([0, 0, 0, -95844, -20220536]\) | \(-1108671232/1369599\) | \(-120284358200810496\) | \([]\) | \(2654208\) | \(1.9709\) | |
310464.bh2 | 310464bh1 | \([0, 0, 0, 9996, 524104]\) | \(1257728/2079\) | \(-182587151932416\) | \([]\) | \(884736\) | \(1.4216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.bh do not have complex multiplication.Modular form 310464.2.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 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.