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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 32760.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32760.b1 | 32760bc4 | \([0, 0, 0, -267123, 38622782]\) | \(2823774927583684/770865531345\) | \(575448035686917120\) | \([2]\) | \(393216\) | \(2.1156\) | |
| 32760.b2 | 32760bc2 | \([0, 0, 0, -97023, -11148478]\) | \(541228074045136/25505687025\) | \(4759973335353600\) | \([2, 2]\) | \(196608\) | \(1.7690\) | |
| 32760.b3 | 32760bc1 | \([0, 0, 0, -95898, -11430403]\) | \(8361897711794176/19963125\) | \(232849890000\) | \([2]\) | \(98304\) | \(1.4224\) | \(\Gamma_0(N)\)-optimal |
| 32760.b4 | 32760bc3 | \([0, 0, 0, 55077, -42876538]\) | \(24751815369116/1078211415645\) | \(-804880508933329920\) | \([2]\) | \(393216\) | \(2.1156\) |
Rank
sage: E.rank()
The elliptic curves in class 32760.b have rank \(1\).
Complex multiplication
The elliptic curves in class 32760.b do not have complex multiplication.Modular form 32760.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
