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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 12495g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12495.j4 | 12495g1 | \([1, 1, 0, 2033, 387136]\) | \(7892485271/552491415\) | \(-65000062483335\) | \([2]\) | \(36864\) | \(1.3300\) | \(\Gamma_0(N)\)-optimal |
12495.j3 | 12495g2 | \([1, 1, 0, -68772, 6660459]\) | \(305759741604409/12646127025\) | \(1487804198364225\) | \([2, 2]\) | \(73728\) | \(1.6766\) | |
12495.j2 | 12495g3 | \([1, 1, 0, -181227, -20846034]\) | \(5595100866606889/1653777286875\) | \(194565244023556875\) | \([2]\) | \(147456\) | \(2.0232\) | |
12495.j1 | 12495g4 | \([1, 1, 0, -1089197, 437075724]\) | \(1214661886599131209/2213451765\) | \(260410386700485\) | \([2]\) | \(147456\) | \(2.0232\) |
Rank
sage: E.rank()
The elliptic curves in class 12495g have rank \(0\).
Complex multiplication
The elliptic curves in class 12495g do not have complex multiplication.Modular form 12495.2.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 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.