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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 239316.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
239316.t1 | 239316t2 | \([0, 1, 0, -7684588, -8201903788]\) | \(1666315860501346000/40252707\) | \(1212336825815808\) | \([2]\) | \(4423680\) | \(2.4143\) | |
239316.t2 | 239316t1 | \([0, 1, 0, -480853, -127957600]\) | \(6532108386304000/31987847133\) | \(60213411637605072\) | \([2]\) | \(2211840\) | \(2.0677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 239316.t have rank \(1\).
Complex multiplication
The elliptic curves in class 239316.t do not have complex multiplication.Modular form 239316.2.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.