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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 23520bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.h3 | 23520bc1 | \([0, -1, 0, -43626, 3411360]\) | \(1219555693504/43758225\) | \(329479130433600\) | \([2, 2]\) | \(73728\) | \(1.5559\) | \(\Gamma_0(N)\)-optimal |
| 23520.h4 | 23520bc2 | \([0, -1, 0, 16399, 12018945]\) | \(1012048064/130203045\) | \(-62743584936775680\) | \([2]\) | \(147456\) | \(1.9025\) | |
| 23520.h2 | 23520bc3 | \([0, -1, 0, -109776, -9315900]\) | \(2428799546888/778248135\) | \(46878778795322880\) | \([2]\) | \(147456\) | \(1.9025\) | |
| 23520.h1 | 23520bc4 | \([0, -1, 0, -691896, 221748696]\) | \(608119035935048/826875\) | \(49807880640000\) | \([2]\) | \(147456\) | \(1.9025\) |
Rank
sage: E.rank()
The elliptic curves in class 23520bc have rank \(1\).
Complex multiplication
The elliptic curves in class 23520bc do not have complex multiplication.Modular form 23520.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
