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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3465.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3465.g1 | 3465t3 | \([1, -1, 1, -19112, 1010724]\) | \(1058993490188089/13182390375\) | \(9609962583375\) | \([4]\) | \(9216\) | \(1.3009\) | |
3465.g2 | 3465t2 | \([1, -1, 1, -2237, -15276]\) | \(1697509118089/833765625\) | \(607815140625\) | \([2, 2]\) | \(4608\) | \(0.95433\) | |
3465.g3 | 3465t1 | \([1, -1, 1, -1832, -29694]\) | \(932288503609/779625\) | \(568346625\) | \([2]\) | \(2304\) | \(0.60776\) | \(\Gamma_0(N)\)-optimal |
3465.g4 | 3465t4 | \([1, -1, 1, 8158, -123384]\) | \(82375335041831/56396484375\) | \(-41113037109375\) | \([2]\) | \(9216\) | \(1.3009\) |
Rank
sage: E.rank()
The elliptic curves in class 3465.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3465.g do not have complex multiplication.Modular form 3465.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.