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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 102960.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.cp1 | 102960bl4 | \([0, 0, 0, -317307, 68796106]\) | \(2366492816943218/23562825\) | \(35179109222400\) | \([4]\) | \(655360\) | \(1.7589\) | |
| 102960.cp2 | 102960bl3 | \([0, 0, 0, -71787, -6258566]\) | \(27403349188178/4524609375\) | \(6755205600000000\) | \([2]\) | \(655360\) | \(1.7589\) | |
| 102960.cp3 | 102960bl2 | \([0, 0, 0, -20307, 1020706]\) | \(1240605018436/115025625\) | \(85866168960000\) | \([2, 2]\) | \(327680\) | \(1.4123\) | |
| 102960.cp4 | 102960bl1 | \([0, 0, 0, 1473, 75454]\) | \(1893932336/14274975\) | \(-2664052934400\) | \([2]\) | \(163840\) | \(1.0658\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.cp have rank \(2\).
Complex multiplication
The elliptic curves in class 102960.cp do not have complex multiplication.Modular form 102960.2.a.cp
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.
