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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 463680.iz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.iz1 | 463680iz1 | \([0, 0, 0, -2975052, 1973690224]\) | \(15238420194810961/12619514880\) | \(2411626849244282880\) | \([2]\) | \(10321920\) | \(2.4556\) | \(\Gamma_0(N)\)-optimal |
463680.iz2 | 463680iz2 | \([0, 0, 0, -2329932, 2853375856]\) | \(-7319577278195281/14169067365600\) | \(-2707750940710640025600\) | \([2]\) | \(20643840\) | \(2.8022\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.iz have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.iz do not have complex multiplication.Modular form 463680.2.a.iz
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.