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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 257600.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.ct1 | 257600ct4 | \([0, 0, 0, -344300, -77758000]\) | \(4407931365156/100625\) | \(103040000000000\) | \([2]\) | \(983040\) | \(1.8024\) | |
| 257600.ct2 | 257600ct3 | \([0, 0, 0, -92300, 9658000]\) | \(84923690436/9794435\) | \(10029501440000000\) | \([2]\) | \(983040\) | \(1.8024\) | |
| 257600.ct3 | 257600ct2 | \([0, 0, 0, -22300, -1122000]\) | \(4790692944/648025\) | \(165894400000000\) | \([2, 2]\) | \(491520\) | \(1.4558\) | |
| 257600.ct4 | 257600ct1 | \([0, 0, 0, 2200, -93000]\) | \(73598976/276115\) | \(-4417840000000\) | \([2]\) | \(245760\) | \(1.1092\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.ct do not have complex multiplication.Modular form 257600.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
