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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 479370t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479370.t4 | 479370t1 | \([1, 1, 0, -8427, 504621]\) | \(-111284641/123120\) | \(-73234647281520\) | \([2]\) | \(2322432\) | \(1.3550\) | \(\Gamma_0(N)\)-optimal* |
479370.t3 | 479370t2 | \([1, 1, 0, -159807, 24513489]\) | \(758800078561/324900\) | \(193258096992900\) | \([2, 2]\) | \(4644864\) | \(1.7016\) | \(\Gamma_0(N)\)-optimal* |
479370.t1 | 479370t3 | \([1, 1, 0, -2556657, 1572399219]\) | \(3107086841064961/570\) | \(339049292970\) | \([2]\) | \(9289728\) | \(2.0482\) | \(\Gamma_0(N)\)-optimal* |
479370.t2 | 479370t4 | \([1, 1, 0, -185037, 16222911]\) | \(1177918188481/488703750\) | \(290692387560153750\) | \([2]\) | \(9289728\) | \(2.0482\) |
Rank
sage: E.rank()
The elliptic curves in class 479370t have rank \(1\).
Complex multiplication
The elliptic curves in class 479370t do not have complex multiplication.Modular form 479370.2.a.t
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 Cremona 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 Cremona labels.