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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 374790.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374790.cp1 | 374790cp4 | \([1, 1, 1, -35999080, -83150171395]\) | \(5813367198762565441/6483117420\) | \(5753790574605223020\) | \([2]\) | \(35389440\) | \(2.8856\) | |
| 374790.cp2 | 374790cp2 | \([1, 1, 1, -2267980, -1278045475]\) | \(1453688056967041/47358464400\) | \(42030811481507456400\) | \([2, 2]\) | \(17694720\) | \(2.5390\) | |
| 374790.cp3 | 374790cp1 | \([1, 1, 1, -345980, 50440925]\) | \(5160676199041/1740960000\) | \(1545108408473760000\) | \([4]\) | \(8847360\) | \(2.1925\) | \(\Gamma_0(N)\)-optimal |
| 374790.cp4 | 374790cp3 | \([1, 1, 1, 711120, -4390609155]\) | \(44810747703359/9410661568620\) | \(-8351996782795484090220\) | \([2]\) | \(35389440\) | \(2.8856\) |
Rank
sage: E.rank()
The elliptic curves in class 374790.cp have rank \(1\).
Complex multiplication
The elliptic curves in class 374790.cp do not have complex multiplication.Modular form 374790.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
