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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 117325h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117325.m2 | 117325h1 | \([0, 1, 1, -1203, -15326]\) | \(163840/13\) | \(15289911325\) | \([]\) | \(82944\) | \(0.69779\) | \(\Gamma_0(N)\)-optimal |
117325.m1 | 117325h2 | \([0, 1, 1, -19253, 1018939]\) | \(671088640/2197\) | \(2583995013925\) | \([]\) | \(248832\) | \(1.2471\) |
Rank
sage: E.rank()
The elliptic curves in class 117325h have rank \(1\).
Complex multiplication
The elliptic curves in class 117325h do not have complex multiplication.Modular form 117325.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.