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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 35280.ec
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.ec1 | 35280dk2 | \([0, 0, 0, -12659787, -17337462534]\) | \(68971442301/400\) | \(1301348428318310400\) | \([2]\) | \(1032192\) | \(2.6660\) | |
| 35280.ec2 | 35280dk1 | \([0, 0, 0, -805707, -260474886]\) | \(17779581/1280\) | \(4164314970618593280\) | \([2]\) | \(516096\) | \(2.3195\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.ec have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.ec do not have complex multiplication.Modular form 35280.2.a.ec
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
