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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 12696.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.h1 | 12696a2 | \([0, -1, 0, -24676968, -47174799204]\) | \(10963069081334500/1156923\) | \(175376511804976128\) | \([2]\) | \(473088\) | \(2.7371\) | |
12696.h2 | 12696a1 | \([0, -1, 0, -1538508, -740537676]\) | \(-10627137250000/110008287\) | \(-4169004688233508608\) | \([2]\) | \(236544\) | \(2.3905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12696.h have rank \(0\).
Complex multiplication
The elliptic curves in class 12696.h do not have complex multiplication.Modular form 12696.2.a.h
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.