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SageMath
E = EllipticCurve("jq1")
E.isogeny_class()
Elliptic curves in class 114240jq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
114240.ji4 | 114240jq1 | \([0, 1, 0, 895, -17025]\) | \(302111711/669375\) | \(-175472640000\) | \([2]\) | \(131072\) | \(0.84172\) | \(\Gamma_0(N)\)-optimal |
114240.ji3 | 114240jq2 | \([0, 1, 0, -7105, -191425]\) | \(151334226289/28676025\) | \(7517247897600\) | \([2, 2]\) | \(262144\) | \(1.1883\) | |
114240.ji2 | 114240jq3 | \([0, 1, 0, -34305, 2262015]\) | \(17032120495489/1339001685\) | \(351011257712640\) | \([2]\) | \(524288\) | \(1.5349\) | |
114240.ji1 | 114240jq4 | \([0, 1, 0, -107905, -13678465]\) | \(530044731605089/26309115\) | \(6896776642560\) | \([2]\) | \(524288\) | \(1.5349\) |
Rank
sage: E.rank()
The elliptic curves in class 114240jq have rank \(0\).
Complex multiplication
The elliptic curves in class 114240jq do not have complex multiplication.Modular form 114240.2.a.jq
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.