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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 20328.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20328.bc1 | 20328g2 | \([0, 1, 0, -392, 2352]\) | \(2450086/441\) | \(1202116608\) | \([2]\) | \(7680\) | \(0.46133\) | |
20328.bc2 | 20328g1 | \([0, 1, 0, 48, 240]\) | \(8788/21\) | \(-28621824\) | \([2]\) | \(3840\) | \(0.11475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20328.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 20328.bc do not have complex multiplication.Modular form 20328.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.