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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 23520i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23520.w3 | 23520i1 | \([0, -1, 0, -310, -608]\) | \(438976/225\) | \(1694145600\) | \([2, 2]\) | \(12288\) | \(0.46311\) | \(\Gamma_0(N)\)-optimal |
23520.w4 | 23520i2 | \([0, -1, 0, 1160, -5900]\) | \(2863288/1875\) | \(-112943040000\) | \([2]\) | \(24576\) | \(0.80969\) | |
23520.w2 | 23520i3 | \([0, -1, 0, -2760, 56232]\) | \(38614472/405\) | \(24395696640\) | \([2]\) | \(24576\) | \(0.80969\) | |
23520.w1 | 23520i4 | \([0, -1, 0, -3985, -95423]\) | \(14526784/15\) | \(7228354560\) | \([2]\) | \(24576\) | \(0.80969\) |
Rank
sage: E.rank()
The elliptic curves in class 23520i have rank \(1\).
Complex multiplication
The elliptic curves in class 23520i do not have complex multiplication.Modular form 23520.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.