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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 30345t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.k2 | 30345t1 | \([1, 0, 0, 894279, -1344074760]\) | \(16098893047132187167/168182866341984375\) | \(-826282422338169234375\) | \([2]\) | \(1013760\) | \(2.6947\) | \(\Gamma_0(N)\)-optimal |
30345.k1 | 30345t2 | \([1, 0, 0, -14163216, -19054700379]\) | \(63953244990201015504593/5088175635498046875\) | \(24998206897201904296875\) | \([2]\) | \(2027520\) | \(3.0413\) |
Rank
sage: E.rank()
The elliptic curves in class 30345t have rank \(0\).
Complex multiplication
The elliptic curves in class 30345t do not have complex multiplication.Modular form 30345.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.