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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 384366.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
384366.t1 | 384366t2 | \([1, 0, 0, -14382845, 21055187199]\) | \(-30526075007211889/103499257854\) | \(-1115640786799960443966\) | \([]\) | \(20763848\) | \(2.9027\) | |
384366.t2 | 384366t1 | \([1, 0, 0, -2255, -14232711]\) | \(-117649/8118144\) | \(-87507222247829376\) | \([]\) | \(2966264\) | \(1.9298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 384366.t have rank \(0\).
Complex multiplication
The elliptic curves in class 384366.t do not have complex multiplication.Modular form 384366.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.