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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 158400.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.r1 | 158400kd3 | \([0, 0, 0, -26393846700, 1650339826526000]\) | \(680995599504466943307169/52207031250000000\) | \(155889360000000000000000000000\) | \([2]\) | \(330301440\) | \(4.6498\) | |
| 158400.r2 | 158400kd2 | \([0, 0, 0, -1759478700, 22155907934000]\) | \(201738262891771037089/45727545600000000\) | \(136541719520870400000000000000\) | \([2, 2]\) | \(165150720\) | \(4.3032\) | |
| 158400.r3 | 158400kd1 | \([0, 0, 0, -579830700, -5077445794000]\) | \(7220044159551112609/448454983680000\) | \(1339079405988741120000000000\) | \([2]\) | \(82575360\) | \(3.9567\) | \(\Gamma_0(N)\)-optimal |
| 158400.r4 | 158400kd4 | \([0, 0, 0, 4000521300, 136906627934000]\) | \(2371297246710590562911/4084000833203280000\) | \(-12194761143931662827520000000000\) | \([2]\) | \(330301440\) | \(4.6498\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.r have rank \(0\).
Complex multiplication
The elliptic curves in class 158400.r do not have complex multiplication.Modular form 158400.2.a.r
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.
