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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 75504bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75504.p1 | 75504bt1 | \([0, -1, 0, -11179240376, 455440355271024]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-190196467981782397994864738304\) | \([]\) | \(101606400\) | \(4.5279\) | \(\Gamma_0(N)\)-optimal |
| 75504.p2 | 75504bt2 | \([0, -1, 0, 31659580264, -28583022592376976]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-354969997597074999409315326120812544\) | \([]\) | \(711244800\) | \(5.5009\) |
Rank
sage: E.rank()
The elliptic curves in class 75504bt have rank \(0\).
Complex multiplication
The elliptic curves in class 75504bt do not have complex multiplication.Modular form 75504.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
