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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 273600.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.t1 | 273600t2 | \([0, 0, 0, -434700, 72414000]\) | \(901428696/296875\) | \(2991816000000000000\) | \([2]\) | \(4423680\) | \(2.2481\) | |
273600.t2 | 273600t1 | \([0, 0, 0, 78300, 7776000]\) | \(42144192/45125\) | \(-56844504000000000\) | \([2]\) | \(2211840\) | \(1.9016\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.t have rank \(2\).
Complex multiplication
The elliptic curves in class 273600.t do not have complex multiplication.Modular form 273600.2.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 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.